Data to 7 Oct 2026

Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints

arXiv 2010.13581 ↗First posted 26 Oct 2020cs.LG math.DS physics.comp-phcited by 102

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Abstract (arXiv)

Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian of a system rather than the differential equations directly. While these methods encode the constraints of the systems using generalized coordinates, we show that embedding the system into Cartesian coordinates and enforcing the constraints explicitly with Lagrange multipliers dramatically simplifies the learning problem. We introduce a series of challenging chaotic and extended-body systems, including systems with N-pendulums, spring coupling, magnetic fields, rigid rotors, and gyroscopes, to push the limits of current approaches. Our experiments show that Cartesian coordinates with explicit constraints lead to a 100x improvement in accuracy and data efficiency.

Key facts. Cited by 102 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Oct 2020.

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Citing papers per year: 2021: 19; 2022: 30; 2023: 20; 2024: 7; 2025: 10; 2026: 16.

102 papers.

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2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
2022Equivariant Graph Mechanics Networks with Constraintscited by 67
2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 37
2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
2023User-defined Event Sampling and Uncertainty Quantification in Diffusion Models for Physical Dynamical Systemscited by 30
2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
2023Self-Supervised Learning with Lie Symmetries for Partial Differential Equationscited by 29
2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
2021Constraint-based graph network simulatorcited by 27

38 more

2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26
2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
2022Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Networkcited by 22
2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
2021Climate Modeling with Neural Diffusion Equationscited by 20
2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 17
2022Physics-Informed Model-Based Reinforcement Learningcited by 17
2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
2022Learning Hamiltonians of constrained mechanical systemscited by 14
2022Homotopy-based training of NeuralODEs for accurate dynamics discoverycited by 14
2021Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equationscited by 13
2021Applying Machine Learning to Study Fluid Mechanicscited by 13
2022Taylor-Lagrange Neural Ordinary Differential Equations: Toward Fast Training and Evaluation of Neural ODEscited by 13
2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
2022Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networkscited by 11
2025Neural Motion Simulator: Pushing the Limit of World Models in Reinforcement Learningcited by 11
2021Machine-Learning Non-Conservative Dynamics for New-Physics Detectioncited by 10
2022Thermodynamics of learning physical phenomenacited by 10
2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
2025Denoising Hamiltonian Network for Physical Reasoningcited by 10
2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
2021OSCAR: Data-Driven Operational Space Control for Adaptive and Robust Robot Manipulationcited by 7
2022A Review of Machine Learning Methods Applied to Structural Dynamics and Vibroacousticcited by 7
2023Learning to Predict 3D Rotational Dynamics from Images of a Rigid Body with Unknown Mass Distributioncited by 7
2024A Riemannian Framework for Learning Reduced-order Lagrangian Dynamicscited by 7
2022Guaranteed Conformance of Neurosymbolic Models to Natural Constraintscited by 6
2023Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processescited by 6
2023Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftingscited by 6
2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 6
2021SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Visioncited by 5
2022Unifying physical systems' inductive biases in neural ODE using dynamics constraintscited by 5
2024Projected Neural Differential Equations for Learning Constrained Dynamicscited by 5
2022Learning Physics-Consistent Particle Interactionscited by 4

50 most cited of 102 All 102 (JSON)