Data to 7 Oct 2026

Lagrangian Neural Networks

arXiv 2003.04630 ↗First posted 10 Mar 2020cs.LG math.DS physics.comp-phcited by 388

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Abstract (arXiv)

Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the physical sciences, they struggle to learn these symmetries. In this paper, we propose Lagrangian Neural Networks (LNNs), which can parameterize arbitrary Lagrangians using neural networks. In contrast to models that learn Hamiltonians, LNNs do not require canonical coordinates, and thus perform well in situations where canonical momenta are unknown or difficult to compute. Unlike previous approaches, our method does not restrict the functional form of learned energies and will produce energy-conserving models for a variety of tasks. We test our approach on a double pendulum and a relativistic particle, demonstrating energy conservation where a baseline approach incurs dissipation and modeling relativity without canonical coordinates where a Hamiltonian approach fails. Finally, we show how this model can be applied to graphs and continuous systems using a Lagrangian Graph Network, and demonstrate it on the 1D wave equation.

Key facts. Cited by 388 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Mar 2020.

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Citing papers per year: 2020: 1; 2021: 54; 2022: 65; 2023: 42; 2024: 62; 2025: 63; 2026: 101.

388 papers.

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2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
2021Characterizing possible failure modes in physics-informed neural networkscited by 632
2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
2021Neural SDEs as Infinite-Dimensional GANscited by 159
2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
2021gradSim: Differentiable simulation for system identification and visuomotor controlcited by 100
2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
2022Clifford Neural Layers for PDE Modelingcited by 91
2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
2021Beltrami Flow and Neural Diffusion on Graphscited by 84
2024ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEscited by 78

38 more

2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 48
2022Investigating Compounding Prediction Errors in Learned Dynamics Modelscited by 47
2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 46
2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
2024Towards Scientific Discovery with Generative AI: Progress, Opportunities, and Challengescited by 41
2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
2021Continuous-Time Model-Based Reinforcement Learningcited by 39
2021Efficient Differentiable Simulation of Articulated Bodiescited by 38
2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 37
2022A posteriori learning for quasi-geostrophic turbulence parametrizationcited by 36
2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 35
2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
2021Machine-learning hidden symmetriescited by 31
2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
2022Machine Learning for Microcontroller-Class Hardware: A Reviewcited by 28
2023Physics-Informed Computer Vision: A Review and Perspectivescited by 28
2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
2020Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learningcited by 27
2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
2021Constraint-based graph network simulatorcited by 27
2022Do Residual Neural Networks discretize Neural Ordinary Differential Equations?cited by 27
2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26
2023The transformative potential of machine learning for experiments in fluid mechanicscited by 26
2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
2022DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulationscited by 24
2022Continuous MDP Homomorphisms and Homomorphic Policy Gradientcited by 24
2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23

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