mlsanityData to 7 Oct 2026

Stable Port-Hamiltonian Neural Networks

arXiv 2502.02480 ↗First posted 4 Feb 2025cs.LGcited by 13

Not on the map. Why?

Abstract (arXiv)

In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its broad potential applications across science and engineering. However, purely data-driven approaches often struggle with extrapolation and may yield physically implausible forecasts. Furthermore, the learned dynamics can exhibit instabilities, making it difficult to apply such models safely and robustly. This article introduces stable port-Hamiltonian neural networks, a machine learning architecture that incorporates physical biases of energy conservation and dissipation while ensuring global Lyapunov stability of the learned dynamics. Through illustrative and real-world examples, we demonstrate that these strong inductive biases facilitate robust learning of stable dynamics from sparse data, while avoiding instability and surpassing purely data-driven approaches in accuracy and physically meaningful generalization. Furthermore, the model's applicability and potential for data-driven surrogate modeling are showcased on multi-physics simulation data.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 36 of its 62 references that are in the map. First posted on arXiv 4 Feb 2025.

Builds on

36 of 62 references.

References · 36

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018Neural Ordinary Differential Equationscited by 3,733
  3. 2019Hamiltonian Neural Networkscited by 702
  4. 2016Input Convex Neural Networkscited by 407
  5. 2019Augmented Neural ODEscited by 396
  6. 2020Lagrangian Neural Networkscited by 388
  7. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 205
  8. 2020Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systemscited by 160
  9. 2020Learning Stable Deep Dynamics Modelscited by 110
  10. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 87
  11. 2018Optimal Control Via Neural Networks: A Convex Approachcited by 82
  12. 2020Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learningcited by 77
24 more
  1. 2019Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Predictioncited by 67
  2. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
  3. 2020Structure-preserving neural networkscited by 54
  4. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 48
  5. 2020Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problemscited by 45
  6. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  7. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 37
  8. 2020OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principlecited by 35
  9. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  10. 2020Stable Neural Flowscited by 25
  11. 2024tLaSDI: Thermodynamics-informed latent space dynamics identificationcited by 23
  12. 2020Learning Dynamics Models with Stable Invariant Setscited by 18
  13. 2020Forecasting Hamiltonian dynamics without canonical coordinatescited by 17
  14. 2021Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systemscited by 17
  15. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  16. 2022Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networkscited by 17
  17. 2021Almost Surely Stable Deep Dynamicscited by 16
  18. 2023Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversioncited by 9
  19. 2023On the effectiveness of neural priors in modeling dynamical systemscited by 4
  20. 2024Data-driven identification of latent port-Hamiltonian systemscited by 3
  21. 2022Learning Deep Input-Output Stable Dynamicscited by 2
  22. 2022Physics-based Digital Twins for Autonomous Thermal Food Processing: Efficient, Non-intrusive Reduced-order Modelingcited by 2
  23. 2024TwinLab: a framework for data-efficient training of non-intrusive reduced-order models for digital twinscited by 2
  24. 2024Digital twin inference from multi-physical simulation data of DED additive manufacturing processes with neural ODEscited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 11.

13 papers.

Sort:

By area:

  1. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  2. 2026Controlled oscillation modeling using port-Hamiltonian neural networkscited by 1
  3. 2026Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamicscited by 1
  4. 2026HaM-World: Soft-Hamiltonian World Models with Selective Memory for Planningcited by 1
  5. 2025Unlocking the Invisible Urban Traffic Dynamics under Extreme Weather: A New Physics-Constrained Hamiltonian Learning Algorithmcited by 0
  6. 2026Structure- and Stability-Preserving Learning of Port-Hamiltonian Systemscited by 0
  7. 2026Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Controlcited by 0
  8. 2026Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equationscited by 0
  9. 2026Identifying the nonlinear string dynamics with port-Hamiltonian neural networkscited by 0
  10. 2026Latent Laplace Diffusion for Irregular Multivariate Time Seriescited by 0
  11. 2026CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Liftscited by 0
  12. 2026Safe-by-Design Learning via Energy-based Neural Networkscited by 0
1 more
  1. 2026Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibriacited by 0