mlsanityData to 7 Oct 2026

Learning to Control PDEs with Differentiable Physics

arXiv 2001.07457 ↗First posted 21 Jan 2020cs.LG physics.flu-dyn stat.MLcited by 131

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Abstract (arXiv)

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.

Key facts. Cited by 131 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Jan 2020.

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Citing papers per year: 2021: 25; 2022: 30; 2023: 22; 2024: 27; 2025: 11; 2026: 16.

131 papers.

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  1. 2022Liquid Structural State-Space Modelscited by 134
  2. 2021PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physicscited by 100
  3. 2023DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Trainingcited by 76
  4. 2022RoboCraft: Learning to See, Simulate, and Shape Elasto-Plastic Objects with Graph Networkscited by 69
  5. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 65
  6. 2021DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contactcited by 64
  7. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  8. 2021DiffPD: Differentiable Projective Dynamicscited by 62
  9. 2021Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contactcited by 50
  10. 2022NeuPhysics: Editable Neural Geometry and Physics from Monocular Videoscited by 50
  11. 2024MotionCraft: Physics-based Zero-Shot Video Generationcited by 46
  12. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
38 more
  1. 2024ConFIG: Towards Conflict-free Training of Physics Informed Neural Networkscited by 43
  2. 2021NTopo: Mesh-free Topology Optimization using Implicit Neural Representationscited by 41
  3. 2021Solving PDE-constrained Control Problems Using Operator Learningcited by 41
  4. 2022Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizonscited by 39
  5. 2022Differentiable Simulation of Soft Multi-body Systemscited by 39
  6. 2021Efficient Differentiable Simulation of Articulated Bodiescited by 38
  7. 2022Learning to Accelerate Partial Differential Equations via Latent Global Evolutioncited by 38
  8. 2022Learning to Solve PDE-constrained Inverse Problems with Graph Networkscited by 37
  9. 2023Geometric Clifford Algebra Networkscited by 37
  10. 2023FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulationcited by 37
  11. 2022NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fieldscited by 36
  12. 2022A posteriori learning for quasi-geostrophic turbulence parametrizationcited by 36
  13. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  14. 2024Wavelet Diffusion Neural Operatorcited by 28
  15. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  16. 2021Learning neural network potentials from experimental data via Differentiable Trajectory Reweightingcited by 26
  17. 2024Clifford-Steerable Convolutional Neural Networkscited by 24
  18. 2021Causal Navigation by Continuous-time Neural Networkscited by 23
  19. 2023DexDeform: Dexterous Deformable Object Manipulation with Human Demonstrations and Differentiable Physicscited by 23
  20. 2025PDE-Controller: LLMs for Autoformalization and Reasoning of PDEscited by 23
  21. 2022Differentiable Programming for Earth System Modelingcited by 21
  22. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  23. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  24. 2025Sparse identification of nonlinear dynamics and Koopman operators with Shallow Recurrent Decoder Networkscited by 19
  25. 2021Global Transport for Fluid Reconstruction with Learned Self-Supervisioncited by 18
  26. 2024RoboPack: Learning Tactile-Informed Dynamics Models for Dense Packingcited by 18
  27. 2021Learning optimal multigrid smoothers via neural networkscited by 17
  28. 2024DiffPhyCon: A Generative Approach to Control Complex Physical Systemscited by 17
  29. 2021SAGCI-System: Towards Sample-Efficient, Generalizable, Compositional, and Incremental Robot Learningcited by 16
  30. 2022Training Efficient Controllers via Analytic Policy Gradientcited by 16
  31. 2023Solving Inverse Physics Problems with Score Matchingcited by 15
  32. 2024Multi-Fidelity Residual Neural Processes for Scalable Surrogate Modelingcited by 13
  33. 2024SineNet: Learning Temporal Dynamics in Time-Dependent Partial Differential Equationscited by 13
  34. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  35. 2023Disentangled Multi-Fidelity Deep Bayesian Active Learningcited by 11
  36. 2023Almost Equivariance via Lie Algebra Convolutionscited by 10
  37. 2024Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Lawscited by 10
  38. 2024NeuralFluid: Neural Fluidic System Design and Control with Differentiable Simulationcited by 10

50 most cited of 131 All 131 (JSON)