Model-based deep reinforcement learning for accelerated learning from flow simulations (2402.16543v2)
Abstract: In recent years, deep reinforcement learning has emerged as a technique to solve closed-loop flow control problems. Employing simulation-based environments in reinforcement learning enables a priori end-to-end optimization of the control system, provides a virtual testbed for safety-critical control applications, and allows to gain a deep understanding of the control mechanisms. While reinforcement learning has been applied successfully in a number of rather simple flow control benchmarks, a major bottleneck toward real-world applications is the high computational cost and turnaround time of flow simulations. In this contribution, we demonstrate the benefits of model-based reinforcement learning for flow control applications. Specifically, we optimize the policy by alternating between trajectories sampled from flow simulations and trajectories sampled from an ensemble of environment models. The model-based learning reduces the overall training time by up to $85\%$ for the fluidic pinball test case. Even larger savings are expected for more demanding flow simulations.
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Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rohrer, T., Frison, L., Kaupenjohann, L., Scharf, K., Hergenröther, E.: Deep reinforcement learning for heat pump control. In: Arai, K. (ed.) Intelligent Computing, pp. 459–471. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-37717-4_29 Esche and Repke [2020] Esche, E., Repke, J.-U.: Dynamic process operation under demand response – a review of methods and tools. Chemie Ingenieur Technik 92(12), 1898–1909 (2020) https://doi.org/10.1002/cite.202000091 Hucho and Sovran [1993] Hucho, W., Sovran, G.: Aerodynamics of road vehicles. Annual Review of Fluid Mechanics 25(1), 485–537 (1993) https://doi.org/10.1146/annurev.fl.25.010193.002413 Choi et al. [2014] Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Esche, E., Repke, J.-U.: Dynamic process operation under demand response – a review of methods and tools. Chemie Ingenieur Technik 92(12), 1898–1909 (2020) https://doi.org/10.1002/cite.202000091 Hucho and Sovran [1993] Hucho, W., Sovran, G.: Aerodynamics of road vehicles. Annual Review of Fluid Mechanics 25(1), 485–537 (1993) https://doi.org/10.1146/annurev.fl.25.010193.002413 Choi et al. [2014] Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Hucho, W., Sovran, G.: Aerodynamics of road vehicles. Annual Review of Fluid Mechanics 25(1), 485–537 (1993) https://doi.org/10.1146/annurev.fl.25.010193.002413 Choi et al. [2014] Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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[2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. 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[2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. 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[1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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- Rohrer, T., Frison, L., Kaupenjohann, L., Scharf, K., Hergenröther, E.: Deep reinforcement learning for heat pump control. In: Arai, K. (ed.) Intelligent Computing, pp. 459–471. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-37717-4_29 Esche and Repke [2020] Esche, E., Repke, J.-U.: Dynamic process operation under demand response – a review of methods and tools. Chemie Ingenieur Technik 92(12), 1898–1909 (2020) https://doi.org/10.1002/cite.202000091 Hucho and Sovran [1993] Hucho, W., Sovran, G.: Aerodynamics of road vehicles. Annual Review of Fluid Mechanics 25(1), 485–537 (1993) https://doi.org/10.1146/annurev.fl.25.010193.002413 Choi et al. [2014] Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Esche, E., Repke, J.-U.: Dynamic process operation under demand response – a review of methods and tools. Chemie Ingenieur Technik 92(12), 1898–1909 (2020) https://doi.org/10.1002/cite.202000091 Hucho and Sovran [1993] Hucho, W., Sovran, G.: Aerodynamics of road vehicles. Annual Review of Fluid Mechanics 25(1), 485–537 (1993) https://doi.org/10.1146/annurev.fl.25.010193.002413 Choi et al. [2014] Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Hucho, W., Sovran, G.: Aerodynamics of road vehicles. Annual Review of Fluid Mechanics 25(1), 485–537 (1993) https://doi.org/10.1146/annurev.fl.25.010193.002413 Choi et al. [2014] Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. 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[2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. 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[2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Choi, H., Lee, J., Park, H.: Aerodynamics of heavy vehicles. Annual Review of Fluid Mechanics 46(1), 441–468 (2014) https://doi.org/10.1146/annurev-fluid-011212-140616 Viquerat et al. [2022] Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. 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[2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. 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Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. 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[1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. 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[2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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[2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Viquerat, J., Meliga, P., Larcher, A., Hachem, E.: A review on deep reinforcement learning for fluid mechanics: An update. Physics of Fluids 34(11), 111301 (2022) https://doi.org/10.1063/5.0128446 Paris et al. [2021] Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. 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Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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[2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618
- Paris, R., Beneddine, S., Dandois, J.: Robust flow control and optimal sensor placement using deep reinforcement learning. Journal of Fluid Mechanics 913, 25 (2021) https://doi.org/10.1017/jfm.2020.1170 Krogmann [2023] Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Krogmann, T.: Optimal sensor placement for active flow control with deep reinforcement learning (2023). https://doi.org/10.5281/zenodo.7636959 Paris et al. [2023] Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. 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[2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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[2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618
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[2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. 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Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. 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[2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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- Paris, R., Beneddine, S., Dandois, J.: Reinforcement-learning-based actuator selection method for active flow control. Journal of Fluid Mechanics 955, 8 (2023) https://doi.org/10.1017/jfm.2022.1043 Ashton et al. [2016] Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. 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[2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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[2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. 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(2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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- Ashton, N., West, A., Lardeau, S., Revell, A.: Assessment of rans and des methods for realistic automotive models. Computers and Fluids 128, 1–15 (2016) https://doi.org/10.1016/j.compfluid.2016.01.008 Belus et al. [2019] Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. 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Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. 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(2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. 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- Belus, V., Rabault, J., Viquerat, J., Che, Z., Hachem, E., Reglade, U.: Exploiting locality and translational invariance to design effective deep reinforcement learning control of the 1-dimensional unstable falling liquid film. AIP Advances 9(12), 125014 (2019) https://doi.org/10.1063/1.5132378 Vignon et al. [2023] Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. 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Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. 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[2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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[2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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- Vignon, C., Rabault, J., Vasanth, J., Alcántara-Ávila, F., Mortensen, M., Vinuesa, R.: Effective control of two-dimensional Rayleigh–Bénard convection: Invariant multi-agent reinforcement learning is all you need. Physics of Fluids 35(6), 065146 (2023) https://doi.org/10.1063/5.0153181 Dixit and Elsheikh [2023] Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. 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[2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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[2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. 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DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. 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SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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- Dixit, A., Elsheikh, A.H.: Robust optimal well control using an adaptive multigrid reinforcement learning framework. Mathematical Geosciences 55(3), 345–375 (2023) https://doi.org/10.1007/s11004-022-10033-x Moerland et al. [2020] Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. 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Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Moerland, T.M., Broekens, J., Jonker, C.M.: Model-based reinforcement learning: A survey. CoRR abs/2006.16712 (2020) 2006.16712 Kurutach et al. [2018] Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. 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[2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Kurutach, T., Clavera, I., Duan, Y., Tamar, A., Abbeel, P.: Model-ensemble trust-region policy optimization. CoRR abs/1802.10592 (2018) 1802.10592 Rabault et al. [2019] Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. 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[2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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[1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618
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[2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. 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[2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Rabault, J., Kuchta, M., Jensen, A., Réglade, U., Cerardi, N.: Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. Journal of Fluid Mechanics 865, 281–302 (2019) https://doi.org/10.1017/jfm.2019.62 Tokarev et al. [2020] Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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[2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. 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[2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Tokarev, M., Palkin, E., Mullyadzhanov, R.: Deep reinforcement learning control of cylinder flow using rotary oscillations at low reynolds number. Energies 13(22), 5920 (2020) https://doi.org/10.3390/en13225920 Holm [2020] Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Holm, M.: Using reinforcement learning for active flow control. DUO Research Archive (2020). http://hdl.handle.net/10852/79212 Sutton and Barto [2018] Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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[2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. 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[2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618
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[1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Sutton, R.S., Barto, A.G.: Reinforcement Learning, Second Edition: An Introduction. Adaptive Computation and Machine Learning series. MIT Press, ??? (2018). https://books.google.de/books?id=5s-MEAAAQBAJ Schulman et al. [2017] Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. CoRR abs/1707.06347 (2017) 1707.06347 Andrychowicz et al. [2021] Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. 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In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. [2020] Hämäläinen, P., Babadi, A., Ma, X., Lehtinen, J.: Ppo-cma: Proximal policy optimization with covariance matrix adaptation. In: 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6 (2020). https://doi.org/10.1109/MLSP49062.2020.9231618 Andrychowicz, M., Raichuk, A., Stanczyk, P.M., Orsini, M., Girgin, S., Marinier, R., Hussenot, L., Geist, M., Pietquin, O., Michalski, M., Gelly, S., Bachem, O.F.: What matters for on-policy deep actor-critic methods? a large-scale study. In: ICLR (2021). https://openreview.net/pdf?id=nIAxjsniDzg Morales [2020] Morales, M.: Grokking Deep Reinforcement Learning. Manning Publications, ??? (2020). https://books.google.de/books?id=IpHJzAEACAAJ Schäfer et al. [1996] Schäfer, M., Turek, S., Durst, F., Krause, E., Rannacher, R.: In: Hirschel, E.H. (ed.) Benchmark Computations of Laminar Flow Around a Cylinder, pp. 547–566. Vieweg+Teubner Verlag, Wiesbaden (1996) Noack et al. [2016] Noack, B.R., Stankiewicz, W., Morzyński, M., Schmid, P.J.: Recursive dynamic mode decomposition of transient and post-transient wake flows. Journal of Fluid Mechanics 809, 843–872 (2016) https://doi.org/10.1017/jfm.2016.678 Raibaudo et al. [2020] Raibaudo, C., Zhong, P., Noack, B.R., Martinuzzi, R.J.: Machine learning strategies applied to the control of a fluidic pinball. Physics of Fluids 32(1), 015108 (2020) https://doi.org/10.1063/1.5127202 Raff [2022] Raff, E.: Inside Deep Learning: Math, Algorithms, Models. Manning, ??? (2022). https://books.google.de/books?id=s8hhzgEACAAJ Proctor et al. [2016] Proctor, J.L., Brunton, S.L., Kutz, J.N.: Dynamic mode decomposition with control. SIAM Journal on Applied Dynamical Systems 15(1), 142–161 (2016) https://doi.org/10.1137/15M1013857 Hämäläinen et al. 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