Learning to Control PDEs with Differentiable Physics
By Philipp Holl, Vladlen Koltun, Nils Thürey. 2020
231 citations recorded by the source corpus.
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 show that by using a differentiable PDE solver in conjunction with a novel predictor-corrector scheme, we can train neural networks to understand and control complex nonlinear physical systems over long time frames. 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.
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- Rex Ying
- Alvaro Sanchez-Gonzalez
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- Peter W. Battaglia
- Tobias Pfaff
- William L. Hamilton
- Jiaxuan You
- Kiwon Um
Citations in the corpus
- Learning to Simulate Complex Physics with Graph Networks (2020, background): “Several differentiable particle-based simulators have recently appeared, e.g., DiffTaichi (Hu et al., 2019), PhiFlow (Holl et al., 2020), and Jax-MD (Schoenholz & Cubuk, 2019), which can backpropagate gradients through the architecture.”
- Liquid Time-constant Networks (2020, background): “A large number of alternative approaches have tried to improve and stabilize the adjoint method [18], use neural ODEs in specific contexts [47, 35] and to characterize them better [11, 12, 32, 21, 29, 45].”
- Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers (2020, background): “Our work shares the motivation of previous work to use differentiable components at training time [1, 14, 58, 9] and frameworks for differentiable programming [50, 25, 26, 23].”