Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning
Peitz, Sebastian
Stenner, Jan
Chidananda, Vikas
Wallscheid, Oliver
Brunton, Steven L.
Taira, Kunihiko
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
info:eu-repo/semantics/preprint
doc-type:preprint
text
http://purl.org/coar/resource_type/c_816b
https://ris.uni-paderborn.de/record/40171
Peitz S, Stenner J, Chidananda V, Wallscheid O, Brunton SL, Taira K. Distributed Control of Partial Differential Equations UsingĀ Convolutional Reinforcement Learning. <i>arXiv:230110737</i>. Published online 2023.
eng
info:eu-repo/semantics/altIdentifier/arxiv/2301.10737
info:eu-repo/semantics/openAccess