Learning to Control PDEs with Differentiable Physics
This addresses the problem of controlling continuous physical systems with many degrees of freedom for researchers in machine learning and physics, offering a method that extends beyond short time frames and limited parameters, though it appears incremental as it builds on existing differentiable physics approaches.
The paper tackles controlling complex nonlinear physical systems described by partial differential equations (PDEs) over long time frames, presenting a hierarchical predictor-corrector scheme that uses neural networks to plan optimal trajectories and infer control parameters, trained end-to-end with a differentiable PDE solver, and demonstrates success on tasks like the incompressible Navier-Stokes equations.
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations (PDEs) with many degrees of freedom. Existing methods that aim to control the dynamics of such systems are typically limited to relatively short time frames or a small number of interaction parameters. We present a novel hierarchical predictor-corrector scheme which enables neural networks to learn to understand and control complex nonlinear physical systems over long time frames. We propose to split the problem into two distinct tasks: planning and control. To this end, we introduce a predictor network that plans optimal trajectories and a control network that infers the corresponding control parameters. Both stages are trained end-to-end using a differentiable PDE solver. We demonstrate that our method successfully develops an understanding of complex physical systems and learns to control them for tasks involving PDEs such as the incompressible Navier-Stokes equations.