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Mapping out phase diagrams with generative classifiers
Published 26 Jun 2023 in quant-ph, cond-mat.dis-nn, and physics.comp-ph | (2306.14894v2)
Abstract: One of the central tasks in many-body physics is the determination of phase diagrams. However, mapping out a phase diagram generally requires a great deal of human intuition and understanding. To automate this process, one can frame it as a classification task. Typically, classification problems are tackled using discriminative classifiers that explicitly model the probability of the labels for a given sample. Here we show that phase-classification problems are naturally suitable to be solved using generative classifiers based on probabilistic models of the measurement statistics underlying the physical system. Such a generative approach benefits from modeling concepts native to the realm of statistical and quantum physics, as well as recent advances in machine learning. This leads to a powerful framework for the autonomous determination of phase diagrams with little to no human supervision that we showcase in applications to classical equilibrium systems and quantum ground states.
- A. Ng and M. Jordan, On Discriminative vs. Generative Classifiers: A comparison of logistic regression and naive Bayes, in Adv. Neural Inf. Process. Syst., Vol. 14, edited by T. Dietterich, S. Becker, and Z. Ghahramani (MIT Press, 2001).
- D. Wu, L. Wang, and P. Zhang, Solving Statistical Mechanics Using Variational Autoregressive Networks, Phys. Rev. Lett. 122, 080602 (2019).
- U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. 326, 96 (2011).
- G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks, Science 355, 602 (2017).
- N. Goldenfeld, Lectures On Phase Transitions And The Renormalization Group (CRC Press, 2018).
- S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 2011).
- P.-W. Guan and V. Viswanathan, MeltNet: Predicting alloy melting temperature by machine learning, arXiv:2010.14048 (2020).
- J. Carrasquilla and R. G. Melko, Machine learning phases of matter, Nat. Phys. 13, 431 (2017).
- E. P. L. van Nieuwenburg, Y.-H. Liu, and S. D. Huber, Learning phase transitions by confusion, Nat. Phys. 13, 435 (2017).
- S. J. Wetzel and M. Scherzer, Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory, Phys. Rev. B 96, 184410 (2017).
- F. Schäfer and N. Lörch, Vector field divergence of predictive model output as indication of phase transitions, Phys. Rev. E 99, 062107 (2019).
- Y.-H. Liu and E. P. L. van Nieuwenburg, Discriminative Cooperative Networks for Detecting Phase Transitions, Phys. Rev. Lett. 120, 176401 (2018).
- M. J. S. Beach, A. Golubeva, and R. G. Melko, Machine learning vortices at the Kosterlitz-Thouless transition, Phys. Rev. B 97, 045207 (2018).
- P. Suchsland and S. Wessel, Parameter diagnostics of phases and phase transition learning by neural networks, Phys. Rev. B 97, 174435 (2018).
- S. S. Lee and B. J. Kim, Confusion scheme in machine learning detects double phase transitions and quasi-long-range order, Phys. Rev. E 99, 043308 (2019).
- W. Guo, B. Ai, and L. He, Reveal flocking of birds flying in fog by machine learning, arXiv:2005.10505 (2020).
- W. Guo and L. He, Learning phase transitions from regression uncertainty: a new regression-based machine learning approach for automated detection of phases of matter, New J. Phys. 25, 083037 (2023).
- H. Schlömer and A. Bohrdt, Fluctuation based interpretable analysis scheme for quantum many-body snapshots, SciPost Phys. 15, 099 (2023).
- L. Onsager, Crystal Statistics. i. A Two-Dimensional Model with an Order-Disorder Transition, Phys. Rev. 65, 117 (1944).
- J. Arnold and F. Schäfer, Replacing neural networks by optimal analytical predictors for the detection of phase transitions, Phys. Rev. X 12, 031044 (2022).
- I. Goodfellow, NIPS 2016 Tutorial: Generative Adversarial Networks, arXiv:1701.00160 (2016), pp. 9 – 17.
- I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT Press, 2016).
- R. Verresen, R. Moessner, and F. Pollmann, One-dimensional symmetry protected topological phases and their transitions, Phys. Rev. B 96, 165124 (2017).
- H. J. Briegel and R. Raussendorf, Persistent entanglement in arrays of interacting particles, Phys. Rev. Lett. 86, 910 (2001).
- P. Zapletal, N. A. McMahon, and M. J. Hartmann, Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases, arXiv:2307.03711 (2023).
- M. Reh, M. Schmitt, and M. Gärttner, Time-Dependent Variational Principle for Open Quantum Systems with Artificial Neural Networks, Phys. Rev. Lett. 127, 230501 (2021).
- A. M. Gomez, S. F. Yelin, and K. Najafi, Reconstructing Quantum States Using Basis-Enhanced Born Machines, arXiv:2206.01273 (2022).
- A. Seif, M. Hafezi, and C. Jarzynski, Machine learning the thermodynamic arrow of time, Nat. Phys. 17, 105 (2021).
- https://github.com/arnoldjulian/Mapping-out-phase-diagrams-with-generative-classifiers.
- M. Richter-Laskowska, M. Kurpas, and M. M. Maśka, Learning by confusion approach to identification of discontinuous phase transitions, Phys. Rev. E 108, 024113 (2023).
- M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active contour models, Int. J. Comput. Vision 1, 321 (1988).
- D. P. Kingma and J. Ba, Adam: A method for stochastic optimization, arXiv:1412.6980 (2014).
- M. Innes, Flux: Elegant machine learning with Julia, J. Open Source Softw. 3, 602 (2018).
- G. Casella and R. L. Berger, Statistical inference (Duxbury, 2002).
- M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor Software Library for Tensor Network Calculations, SciPost Phys. Codebases , 4 (2022).
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