Distributed Control of Partial Differential Equations Using Convolutional Reinforcement Learning
This work addresses computational bottlenecks in controlling PDEs for applications like fluid dynamics or materials science, offering a scalable and efficient method, though it appears incremental as it builds on existing reinforcement learning and convolutional techniques.
The paper tackles the high computational complexity of distributed reinforcement learning control for partial differential equations (PDEs) by introducing a convolutional framework that exploits translational invariances and finite information velocity, reducing the problem to a multi-agent control task with low-dimensional agents and demonstrating stabilization on PDE examples with minimal computing resources.
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.