mlsanityData to 14 Oct 2026

Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models

arXiv 2102.06794 ↗First posted 12 Feb 2021cs.RO cs.AI cs.LGcited by 34

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Abstract (arXiv)

The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or Hamiltonian dynamics into the neural network architecture. These existing approaches are based on differential equations, which do not allow discontinuity in the states and thereby limit the class of systems one can learn. However, in reality, most physical systems, such as legged robots and robotic manipulators, involve contacts and collisions, which introduce discontinuities in the states. In this paper, we introduce a differentiable contact model, which can capture contact mechanics: frictionless/frictional, as well as elastic/inelastic. This model can also accommodate inequality constraints, such as limits on the joint angles. The proposed contact model extends the scope of Lagrangian and Hamiltonian neural networks by allowing simultaneous learning of contact and system properties. We demonstrate this framework on a series of challenging 2D and 3D physical systems with different coefficients of restitution and friction. The learned dynamics can be used as a differentiable physics simulator for downstream gradient-based optimization tasks, such as planning and control.

Key facts. Cited by 34 papers in the map (data through 14 Oct 2026). Builds on 29 of its 59 references that are in the map. First posted on arXiv 12 Feb 2021.

Builds on

29 of 59 references.

References · 29

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17 more
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 10; 2023: 5; 2024: 3; 2025: 7; 2026: 7.

34 papers.

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  1. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 41
  2. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 39
  3. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  4. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  5. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
  6. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  7. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 18
  8. 2022Physics-Informed Model-Based Reinforcement Learningcited by 18
  9. 2022Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networkscited by 12
  10. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  11. 2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
  12. 2022Differentiable Physics Simulations with Contacts: Do They Have Correct Gradients w.r.t. Position, Velocity and Control?cited by 7
22 more
  1. 2024A Riemannian Framework for Learning Reduced-order Lagrangian Dynamicscited by 7
  2. 2024Learning Neural Differential Algebraic Equations via Operator Splittingcited by 6
  3. 2023Improving Gradient Computation for Differentiable Physics Simulation with Contactscited by 5
  4. 2022ModLaNets: Learning Generalisable Dynamics via Modularity and Physical Inductive Biascited by 4
  5. 2024DEL: Discrete Element Learner for Learning 3D Particle Dynamics with Neural Renderingcited by 4
  6. 2025ProJo4D: Progressive Joint Optimization for Sparse-View Inverse Physics Estimationcited by 4
  7. 2026RigidFormer: Learning Rigid Dynamics using Transformerscited by 3
  8. 2023A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from datacited by 2
  9. 2025Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisionscited by 2
  10. 2025Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approachcited by 2
  11. 2022Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltoniancited by 1
  12. 2023Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Controlcited by 1
  13. 2025EqCollide: Equivariant and Collision-Aware Deformable Objects Neural Simulatorcited by 1
  14. 2025Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurementscited by 1
  15. 2025UniBYD: A Unified Framework for Learning Robotic Manipulation Across Embodiments Beyond Imitation of Human Demonstrationscited by 1
  16. 2026NEXUS: Neural Energy Fields for Physically Consistent Contact-Rich 3D Object Dynamicscited by 1
  17. 2025Hamiltonian Neural PDE Solvers through Functional Approximationcited by 0
  18. 2026Deepmechanicscited by 0
  19. 2026STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matchingcited by 0
  20. 2026LaGSplat: Inferring Physics-Governed Interactive Simulation from Monocular Video Using Latent Lagrangian Gaussian Splattingcited by 0
  21. 2026Conservation Buys Stability and Factoring Buys Counterfactuals in Physical World Modelscited by 0
  22. 2026Stable and Counterfactually Robust Physical World Models from Imposed Structure and Learned Physicscited by 0