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Training all-mechanical neural networks for task learning through in situ backpropagation (2404.15471v1)
Published 23 Apr 2024 in cs.LG and physics.app-ph
Abstract: Recent advances unveiled physical neural networks as promising machine learning platforms, offering faster and more energy-efficient information processing. Compared with extensively-studied optical neural networks, the development of mechanical neural networks (MNNs) remains nascent and faces significant challenges, including heavy computational demands and learning with approximate gradients. Here, we introduce the mechanical analogue of in situ backpropagation to enable highly efficient training of MNNs. We demonstrate that the exact gradient can be obtained locally in MNNs, enabling learning through their immediate vicinity. With the gradient information, we showcase the successful training of MNNs for behavior learning and machine learning tasks, achieving high accuracy in regression and classification. Furthermore, we present the retrainability of MNNs involving task-switching and damage, demonstrating the resilience. Our findings, which integrate the theory for training MNNs and experimental and numerical validations, pave the way for mechanical machine learning hardware and autonomous self-learning material systems.
- Jordan, M.I., Mitchell, T.M.: Machine learning: Trends, perspectives, and prospects. Science 349(6245), 255–260 (2015) Egmont-Petersen et al. [2002] Egmont-Petersen, M., Ridder, D., Handels, H.: Image processing with neural networks—a review. Pattern recognition 35(10), 2279–2301 (2002) Adamopoulou and Moussiades [2020] Adamopoulou, E., Moussiades, L.: Chatbots: History, technology, and applications. Machine Learning with applications 2, 100006 (2020) Turay and Vladimirova [2022] Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Egmont-Petersen, M., Ridder, D., Handels, H.: Image processing with neural networks—a review. Pattern recognition 35(10), 2279–2301 (2002) Adamopoulou and Moussiades [2020] Adamopoulou, E., Moussiades, L.: Chatbots: History, technology, and applications. Machine Learning with applications 2, 100006 (2020) Turay and Vladimirova [2022] Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Adamopoulou, E., Moussiades, L.: Chatbots: History, technology, and applications. Machine Learning with applications 2, 100006 (2020) Turay and Vladimirova [2022] Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Egmont-Petersen, M., Ridder, D., Handels, H.: Image processing with neural networks—a review. Pattern recognition 35(10), 2279–2301 (2002) Adamopoulou and Moussiades [2020] Adamopoulou, E., Moussiades, L.: Chatbots: History, technology, and applications. Machine Learning with applications 2, 100006 (2020) Turay and Vladimirova [2022] Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Adamopoulou, E., Moussiades, L.: Chatbots: History, technology, and applications. Machine Learning with applications 2, 100006 (2020) Turay and Vladimirova [2022] Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Adamopoulou, E., Moussiades, L.: Chatbots: History, technology, and applications. Machine Learning with applications 2, 100006 (2020) Turay and Vladimirova [2022] Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Turay, T., Vladimirova, T.: Toward performing image classification and object detection with convolutional neural networks in autonomous driving systems: A survey. IEEE Access 10, 14076–14119 (2022) Abiodun et al. [2019] Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Abiodun, O.I., Jantan, A., Omolara, A.E., Dada, K.V., Umar, A.M., Linus, O.U., Arshad, H., Kazaure, A.A., Gana, U., Kiru, M.U.: Comprehensive review of artificial neural network applications to pattern recognition. IEEE access 7, 158820–158846 (2019) Carleo et al. [2019] Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Carleo, G., Cirac, I., Cranmer, K., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., Zdeborová, L.: Machine learning and the physical sciences. Reviews of Modern Physics 91(4), 045002 (2019) Amari [1993] Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Amari, S.-i.: Backpropagation and stochastic gradient descent method. Neurocomputing 5(4-5), 185–196 (1993) Lillicrap et al. [2020] Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Lillicrap, T.P., Santoro, A., Marris, L., Akerman, C.J., Hinton, G.: Backpropagation and the brain. Nature Reviews Neuroscience 21(6), 335–346 (2020) Thompson et al. [2020] Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Thompson, N.C., Greenewald, K., Lee, K., Manso, G.F.: The computational limits of deep learning. arXiv preprint arXiv:2007.05558 (2020) Sze et al. [2017] Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Sze, V., Chen, Y.-H., Yang, T.-J., Emer, J.S.: Efficient processing of deep neural networks: A tutorial and survey. Proceedings of the IEEE 105(12), 2295–2329 (2017) Hamerly et al. [2019] Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Hamerly, R., Bernstein, L., Sludds, A., Soljačić, M., Englund, D.: Large-scale optical neural networks based on photoelectric multiplication. Physical Review X 9(2), 021032 (2019) Caulfield and Dolev [2010] Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Caulfield, H.J., Dolev, S.: Why future supercomputing requires optics. Nature Photonics 4(5), 261–263 (2010) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Wave physics as an analog recurrent neural network. Science advances 5(12), 6946 (2019) Wetzstein et al. [2020] Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Wetzstein, G., Ozcan, A., Gigan, S., Fan, S., Englund, D., Soljačić, M., Denz, C., Miller, D.A., Psaltis, D.: Inference in artificial intelligence with deep optics and photonics. Nature 588(7836), 39–47 (2020) Shastri et al. [2021] Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Shastri, B.J., Tait, A.N., Lima, T., Pernice, W.H., Bhaskaran, H., Wright, C.D., Prucnal, P.R.: Photonics for artificial intelligence and neuromorphic computing. Nature Photonics 15(2), 102–114 (2021) Wang et al. [2022] Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Wang, T., Ma, S.-Y., Wright, L.G., Onodera, T., Richard, B.C., McMahon, P.L.: An optical neural network using less than 1 photon per multiplication. Nature Communications 13(1), 123 (2022) Pai et al. [2023] Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Pai, S., Sun, Z., Hughes, T.W., Park, T., Bartlett, B., Williamson, I.A., Minkov, M., Milanizadeh, M., Abebe, N., Morichetti, F., et al.: Experimentally realized in situ backpropagation for deep learning in photonic neural networks. Science 380(6643), 398–404 (2023) Hermans et al. [2015] Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Hermans, M., Burm, M., Van Vaerenbergh, T., Dambre, J., Bienstman, P.: Trainable hardware for dynamical computing using error backpropagation through physical media. Nature communications 6(1), 6729 (2015) Wright et al. [2022] Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Wright, L.G., Onodera, T., Stein, M.M., Wang, T., Schachter, D.T., Hu, Z., McMahon, P.L.: Deep physical neural networks trained with backpropagation. Nature 601(7894), 549–555 (2022) Jiang et al. [2023] Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Jiang, T., Li, T., Huang, H., Peng, Z.-K., He, Q.: Metamaterial-based analog recurrent neural network toward machine intelligence. Physical Review Applied 19(6), 064065 (2023) Hughes et al. [2019] Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Hughes, T.W., Williamson, I.A., Minkov, M., Fan, S.: Forward-mode differentiation of maxwell’s equations. ACS Photonics 6(11), 3010–3016 (2019) Lin et al. [2018] Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Lin, X., Rivenson, Y., Yardimci, N.T., Veli, M., Luo, Y., Jarrahi, M., Ozcan, A.: All-optical machine learning using diffractive deep neural networks. Science 361(6406), 1004–1008 (2018) Lee et al. [2022] Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Lee, R.H., Mulder, E.A., Hopkins, J.B.: Mechanical neural networks: Architected materials that learn behaviors. Science Robotics 7(71), 7278 (2022) Hopkins et al. [2023] Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Hopkins, J.B., Lee, R.H., Sainaghi, P.: Using binary-stiffness beams within mechanical neural-network metamaterials to learn. Smart Materials and Structures 32(3), 035015 (2023) Stern et al. [2020] Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Stern, M., Arinze, C., Perez, L., Palmer, S.E., Murugan, A.: Supervised learning through physical changes in a mechanical system. Proceedings of the National Academy of Sciences 117(26), 14843–14850 (2020) Stern et al. [2021] Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Stern, M., Hexner, D., Rocks, J.W., Liu, A.J.: Supervised learning in physical networks: From machine learning to learning machines. Physical Review X 11(2), 021045 (2021) Stern and Murugan [2023] Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Stern, M., Murugan, A.: Learning without neurons in physical systems. Annual Review of Condensed Matter Physics 14, 417–441 (2023) Altman et al. [2023] Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Altman, L.E., Stern, M., Liu, A.J., Durian, D.J.: Experimental demonstration of coupled learning in elastic networks. arXiv preprint arXiv:2311.00170 (2023) Hughes et al. [2018] Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Hughes, T.W., Minkov, M., Shi, Y., Fan, S.: Training of photonic neural networks through in situ backpropagation and gradient measurement. Optica 5(7), 864–871 (2018) Dillavou et al. [2022] Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Demonstration of decentralized physics-driven learning. Physical Review Applied 18(1), 014040 (2022) Wycoff et al. [2022] Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Wycoff, J.F., Dillavou, S., Stern, M., Liu, A.J., Durian, D.J.: Desynchronous learning in a physics-driven learning network. The Journal of Chemical Physics 156(14) (2022) Good [1956] Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Good, I.: Some terminology and notation in information theory. Proceedings of the IEE-Part C: Monographs 103(3), 200–204 (1956) Fisher [1988] Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Fisher, R.A.: Iris. UCI Machine Learning Repository. DOI: https://doi.org/10.24432/C56C76 (1988) Beygelzimer et al. [2005] Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Beygelzimer, A., Grinstein, G., Linsker, R., Rish, I.: Improving network robustness by edge modification. Physica A: Statistical Mechanics and its Applications 357(3-4), 593–612 (2005) Dekker and Colbert [2004] Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Dekker, A.H., Colbert, B.D.: Network robustness and graph topology. In: Proceedings of the 27th Australasian Conference on Computer science-Volume 26, pp. 359–368 (2004) Kalampokis et al. [2003] Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Kalampokis, A., Kotsavasiloglou, C., Argyrakis, P., Baloyannis, S.: Robustness in biological neural networks. Physica A: Statistical Mechanics and its Applications 317(3-4), 581–590 (2003) Eluyode and Akomolafe [2013] Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Eluyode, O., Akomolafe, D.T.: Comparative study of biological and artificial neural networks. European Journal of Applied Engineering and Scientific Research 2(1), 36–46 (2013) Zhang et al. [2023] Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Zhang, W., Zhou, J., Jia, Y., Chen, J., Pu, Y., Fan, R., Meng, F., Ge, Q., Lu, Y.: Magnetoactive microlattice metamaterials with highly tunable stiffness and fast response rate. NPG Asia Materials 15(1), 45 (2023) Poon and Hopkins [2019] Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Poon, R., Hopkins, J.B.: Phase-changing metamaterial capable of variable stiffness and shape morphing. Advanced Engineering Materials 21(12), 1900802 (2019) Stowers et al. [2015] Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Stowers, R.S., Allen, S.C., Suggs, L.J.: Dynamic phototuning of 3d hydrogel stiffness. Proceedings of the National Academy of Sciences 112(7), 1953–1958 (2015) Poggio et al. [2020] Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Poggio, T., Banburski, A., Liao, Q.: Theoretical issues in deep networks. Proceedings of the National Academy of Sciences 117(48), 30039–30045 (2020) Hedrick [2008] Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Hedrick, T.L.: Software techniques for two-and three-dimensional kinematic measurements of biological and biomimetic systems. Bioinspiration & biomimetics 3(3), 034001 (2008) Li et al. [2022] Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Li, S., Roger, L.M., Klein-Seetharaman, J., Lewinski, N.A., Yang, J.: Spatiotemporal dynamics of coral polyps on a fluidic platform. Physical Review Applied 18(2), 024078 (2022) Li et al. [2023] Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023) Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
- Li, S., Roger, L.M., Klein-Seetharaman, J., Cowen, L.J., Lewinski, N.A., Yang, J.: Data-driven discovery of spatiotemporal coherent patterns in pulsating soft coral tentacle motion with dynamic mode decomposition. Physical Review Research 5(1), 013175 (2023)
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