preprint
Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning
Sebastian
Peitz
author 474270000-0002-3389-793X
Jan
Stenner
author 65520
Vikas
Chidananda
author
Oliver
Wallscheid
author 11291https://orcid.org/0000-0001-9362-8777
Steven L.
Brunton
author
Kunihiko
Taira
author
655
department
We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs). Exploiting translational invariances, the high-dimensional distributed control problem can be transformed into a multi-agent control problem with many identical, uncoupled agents. Furthermore, using the fact that information is transported with finite velocity in many cases, the dimension of the agents' environment can be drastically reduced using a convolution operation over the state space of the PDE. In this setting, the complexity can be flexibly adjusted via the kernel width or by using a stride greater than one. Moreover, scaling from smaller to larger systems -- or the transfer between different domains -- becomes a straightforward task requiring little effort. We demonstrate the performance of the proposed framework using several PDE examples with increasing complexity, where stabilization is achieved by training a low-dimensional deep deterministic policy gradient agent using minimal computing resources.
2023
eng
arXiv:2301.10737
2301.10737
Peitz, S., Stenner, J., Chidananda, V., Wallscheid, O., Brunton, S. L., & Taira, K. (2023). Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning. In <i>arXiv:2301.10737</i>.
Peitz S, Stenner J, Chidananda V, Wallscheid O, Brunton SL, Taira K. Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning. <i>arXiv:230110737</i>. Published online 2023.
Peitz, Sebastian, et al. “Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning.” <i>ArXiv:2301.10737</i>, 2023.
S. Peitz, J. Stenner, V. Chidananda, O. Wallscheid, S. L. Brunton, and K. Taira, “Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning,” <i>arXiv:2301.10737</i>. 2023.
Peitz, Sebastian, Jan Stenner, Vikas Chidananda, Oliver Wallscheid, Steven L. Brunton, and Kunihiko Taira. “Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning.” <i>ArXiv:2301.10737</i>, 2023.
@article{Peitz_Stenner_Chidananda_Wallscheid_Brunton_Taira_2023, title={Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning}, journal={arXiv:2301.10737}, author={Peitz, Sebastian and Stenner, Jan and Chidananda, Vikas and Wallscheid, Oliver and Brunton, Steven L. and Taira, Kunihiko}, year={2023} }
S. Peitz, J. Stenner, V. Chidananda, O. Wallscheid, S.L. Brunton, K. Taira, ArXiv:2301.10737 (2023).
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