mlsanityData to 7 Oct 2026

Deconstructing the Inductive Biases of Hamiltonian Neural Networks

arXiv 2202.04836 ↗First posted 10 Feb 2022cs.LG math.DS physics.data-ancited by 31

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Abstract (arXiv)

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world systems, such as those that don't conserve energy or contain contacts, a common setting for robotics and reinforcement learning. In this paper, we examine the inductive biases that make physics-inspired models successful in practice. We show that, contrary to conventional wisdom, the improved generalization of HNNs is the result of modeling acceleration directly and avoiding artificial complexity from the coordinate system, rather than symplectic structure or energy conservation. We show that by relaxing the inductive biases of these models, we can match or exceed performance on energy-conserving systems while dramatically improving performance on practical, non-conservative systems. We extend this approach to constructing transition models for common Mujoco environments, showing that our model can appropriately balance inductive biases with the flexibility required for model-based control.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 31 of its 40 references that are in the map. First posted on arXiv 10 Feb 2022.

Builds on

31 of 40 references.

References · 31

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  2. 2016WaveNet: A Generative Model for Raw Audiocited by 1,710
  3. 2019Simplifying Graph Convolutional Networkscited by 1,470
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  6. 2018Deep Reinforcement Learning in a Handful of Trials using Probabilistic Dynamics Modelscited by 748
  7. 2019Hamiltonian Neural Networkscited by 702
  8. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  9. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  10. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
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  12. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
19 more
  1. 2019Exploring Model-based Planning with Policy Networkscited by 90
  2. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
  3. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
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  5. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  6. 2020On the model-based stochastic value gradient for continuous reinforcement learningcited by 46
  7. 2020Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Datacited by 40
  8. 2020Trust the Model When It Is Confident: Masked Model-based Actor-Criticcited by 36
  9. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
  10. 2020Nonseparable Symplectic Neural Networkscited by 31
  11. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  12. 2020Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systemscited by 24
  13. 2020Structured Mechanical Models for Robot Learning and Controlcited by 21
  14. 2020DyNODE: Neural Ordinary Differential Equations for Dynamics Modeling in Continuous Controlcited by 17
  15. 2019Neural Canonical Transformation with Symplectic Flowscited by 16
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  17. 2021Physics-Augmented Learning: A New Paradigm Beyond Physics-Informed Learningcited by 11
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  19. 2021Machine-Learning Non-Conservative Dynamics for New-Physics Detectioncited by 10

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 12; 2023: 11; 2024: 2; 2025: 5; 2026: 1.

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  1. 2024ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEscited by 78
  2. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  3. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 25
  4. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
  5. 2022Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Networkcited by 22
  6. 2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
  7. 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
  8. 2022Homotopy-based training of NeuralODEs for accurate dynamics discoverycited by 14
  9. 2022Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networkscited by 11
  10. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  11. 2022Thermodynamics of learning physical phenomenacited by 10
  12. 2023Symmetry-invariant quantum machine learning force fieldscited by 8
19 more
  1. 2023Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processescited by 6
  2. 2022Unifying physical systems' inductive biases in neural ODE using dynamics constraintscited by 5
  3. 2022Learning Trajectories of Hamiltonian Systems with Neural Networkscited by 4
  4. 2025Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraintscited by 4
  5. 2022Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learningcited by 3
  6. 2023Discovering interpretable Lagrangian of dynamical systems from datacited by 3
  7. 2025Dynami-CAL GraphNet: A Physics-Informed Graph Neural Network Conserving Linear and Angular Momentum for Dynamical Systemscited by 3
  8. 2025Investigating Lagrangian Neural Networks for Infinite Horizon Planning in Quadrupedal Locomotioncited by 3
  9. 2025Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systemscited by 3
  10. 2023Graph Neural Stochastic Differential Equations for Learning Brownian Dynamicscited by 2
  11. 2023A Bayesian framework for discovering interpretable Lagrangian of dynamical systems from datacited by 2
  12. 2022Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltoniancited by 1
  13. 2023Discovering Symbolic Laws Directly from Trajectories with Hamiltonian Graph Neural Networkscited by 1
  14. 2023Separable Hamiltonian Neural Networkscited by 1
  15. 2022KeyCLD: Learning Constrained Lagrangian Dynamics in Keypoint Coordinates from Imagescited by 0
  16. 2023A Comparative Evaluation of Additive Separability Tests for Physics-Informed Machine Learningcited by 0
  17. 2024Poisson-Dirac Neural Networks for Modeling Coupled Dynamical Systems across Domainscited by 0
  18. 2025Hamiltonian Neural PDE Solvers through Functional Approximationcited by 0
  19. 2026STRIDE: Structured Lagrangian and Stochastic Residual Dynamics via Flow Matchingcited by 0