Learning to Control PDEs with Differentiable Physics

TL;DR

This paper introduces a hierarchical neural network approach with a differentiable PDE solver to learn long-term control of complex nonlinear physical systems described by PDEs, such as Navier-Stokes equations.

Contribution

It presents a novel predictor-corrector scheme that separates planning and control tasks, enabling neural networks to understand and manipulate PDE-governed systems over extended periods.

Findings

Successfully controls complex PDE systems like Navier-Stokes.

Learns long-term trajectories and control parameters.

End-to-end training with differentiable PDEs enhances understanding.

Abstract

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.