Abstract

Predicting outcomes and planning interactions with the physical world are longstanding 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 predictorcorrector 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 controlling. To that end we introduce a predictor network that plans optimal trajectories and a controller network that infers the corresponding control parameters. Both stages are trained end-to-end using a differentiable PDF solver. We demonstrate that our method successfully develops an understanding of complex physical systems and learns to control them for tasks involving multiple PDEs, including the incompressible Navier-Stokes equations.