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Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems

arXiv 2107.08024 ↗First posted 16 Jul 2021cs.LG nlin.CD physics.comp-phcited by 67

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Abstract (arXiv)

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known apriori. Despite this success, many real world dynamical systems are non-autonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such non-autonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

Key facts. Cited by 67 papers in the map (data through 14 Oct 2026). Builds on 15 of its 33 references that are in the map. First posted on arXiv 16 Jul 2021.

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15 of 33 references.

References · 15

  1. 2018BERT: Pre-training of Deep Bidirectional Transformers for Language Understandingcited by 40,399
  2. 2017Mask R-CNNcited by 7,277
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2020Learning to Simulate Complex Physics with Graph Networkscited by 880
  5. 2019Hamiltonian Neural Networkscited by 712
  6. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
  7. 2020Lagrangian Neural Networkscited by 398
  8. 2019Augmented Neural ODEscited by 397
  9. 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 373
  10. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  11. 2018Graph networks as learnable physics engines for inference and controlcited by 244
  12. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
3 more
  1. 2019Hamiltonian Generative Networkscited by 137
  2. 2019Hamiltonian Graph Networks with ODE Integratorscited by 108
  3. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 79

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 3; 2022: 6; 2023: 9; 2024: 8; 2025: 13; 2026: 28.

67 papers.

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  1. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  2. 2022Thermodynamics-informed graph neural networkscited by 33
  3. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  4. 2021Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modelingcited by 27
  5. 2021Noether Networks: Meta-Learning Useful Conserved Quantitiescited by 26
  6. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
  7. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 18
  8. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 18
  9. 2023Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Priorcited by 15
  10. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  11. 2022Learning reversible symplectic dynamicscited by 11
  12. 2022Thermodynamics of learning physical phenomenacited by 10
38 more
  1. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  2. 2023How to Learn and Generalize From Three Minutes of Data: Physics-Constrained and Uncertainty-Aware Neural Stochastic Differential Equationscited by 10
  3. 2023Discussing the Spectrum of Physics-Enhanced Machine Learning; a Survey on Structural Mechanics Applicationscited by 7
  4. 2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 7
  5. 2025Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamicscited by 6
  6. 2023Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Modelscited by 5
  7. 2024Predicting Ship Responses in Different Seaways using a Generalizable Force Correcting Machine Learning Methodcited by 4
  8. 2024Physics-Constrained Learning for PDE Systems with Uncertainty Quantified Port-Hamiltonian Modelscited by 4
  9. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  10. 2023Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamicscited by 3
  11. 2024Data-driven identification of latent port-Hamiltonian systemscited by 3
  12. 2025Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systemscited by 3
  13. 2025Identifiable learning of dissipative dynamicscited by 3
  14. 2024Physics-informed Imitative Reinforcement Learning for Real-world Drivingcited by 2
  15. 2024Training Hamiltonian neural networks without backpropagationcited by 2
  16. 2024Neural Port-Hamiltonian Differential Algebraic Equations for Compositional Learning of Electrical Networkscited by 2
  17. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  18. 2025Meta-learning Structure-Preserving Dynamicscited by 2
  19. 2025Data-efficient Kernel Methods for Learning Hamiltonian Systemscited by 2
  20. 2026PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecastingcited by 2
  21. 2026Metriplector: From Field Theory to Neural Architecturecited by 2
  22. 2023Pseudo-Hamiltonian system identificationcited by 1
  23. 2023Separable Hamiltonian Neural Networkscited by 1
  24. 2025Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Datacited by 1
  25. 2025Learning Physically Consistent Lagrangian Control Models Without Acceleration Measurementscited by 1
  26. 2026Physics-informed Diffusion Mamba Transformer for Real-world Drivingcited by 1
  27. 2026Controlled oscillation modeling using port-Hamiltonian neural networkscited by 1
  28. 2026PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Networkcited by 1
  29. 2026NEXUS: Neural Energy Fields for Physically Consistent Contact-Rich 3D Object Dynamicscited by 1
  30. 2026CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systemscited by 1
  31. 2026History-informed Lagrangian Neural Networkscited by 1
  32. 2024Neural Operators Meet Energy-based Theory: Operator Learning for Hamiltonian and Dissipative PDEscited by 0
  33. 2025On the Generalization of Data-Assisted Control in port-Hamiltonian Systems (DAC-pH)cited by 0
  34. 2025Let Physics Guide Your Protein Flows: Topology-aware Unfolding and Generationcited by 0
  35. 2025Unlocking the Invisible Urban Traffic Dynamics under Extreme Weather: A New Physics-Constrained Hamiltonian Learning Algorithmcited by 0
  36. 2026Gradient Networks for Universal Magnetic Modeling of Synchronous Machinescited by 0
  37. 2026An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulationcited by 0
  38. 2026Structure- and Stability-Preserving Learning of Port-Hamiltonian Systemscited by 0

50 most cited of 67 All 67 (JSON)