Learning to Control PDEs with Differentiable Physics

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.

Published as a conference paper at ICLR 2020. Main text: 10 pages, 6 figures, 3 tables. Total: 28 pages, 18 figures

References in corpus (1)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library

Cited by in corpus (8)

• Lagrangian Neural Style Transfer for Fluids
• Causal Navigation by Continuous-time Neural Networks
• PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics
• A composable autoencoder-based iterative algorithm for accelerating numerical simulations
• A Latent space solver for PDE generalization
• Differentiable Spline Approximations
• Additive manufacturing process design with differentiable simulations
• Physics-Aware Downsampling with Deep Learning for Scalable Flood Modeling