# Stable Port-Hamiltonian Neural Networks

arXiv: https://arxiv.org/abs/2502.02480 · HTML: https://mlsanity.com/paper/2502.02480/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 62 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 30 of 36)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems](https://mlsanity.com/paper/2003.04919/) (2020)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning](https://mlsanity.com/paper/2002.08860/) (2020)
- [Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction](https://mlsanity.com/paper/1905.10866/) (2019)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [Structure-preserving neural networks](https://mlsanity.com/paper/2004.04653/) (2020)
- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems](https://mlsanity.com/paper/2010.14685/) (2020)
- [Physics-Guided Deep Learning for Dynamical Systems: A Survey](https://mlsanity.com/paper/2107.01272/) (2021)
- [Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks](https://mlsanity.com/paper/2012.03133/) (2020)
- [OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle](https://mlsanity.com/paper/2009.02327/) (2020)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Stable Neural Flows](https://mlsanity.com/paper/2003.08063/) (2020)
- [tLaSDI: Thermodynamics-informed latent space dynamics identification](https://mlsanity.com/paper/2403.05848/) (2024)
- [Learning Dynamics Models with Stable Invariant Sets](https://mlsanity.com/paper/2006.08935/) (2020)
- [Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces](https://mlsanity.com/paper/2206.02660/) (2022)
- [Compositional Learning of Dynamical System Models Using Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2212.00893/) (2022)
- [Forecasting Hamiltonian dynamics without canonical coordinates](https://mlsanity.com/paper/2010.15201/) (2020)
- [Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systems](https://mlsanity.com/paper/2110.14296/) (2021)
- [Almost Surely Stable Deep Dynamics](https://mlsanity.com/paper/2103.14722/) (2021)
- [Gradient-free training of neural ODEs for system identification and control using ensemble Kalman inversion](https://mlsanity.com/paper/2307.07882/) (2023)

## Built on by (most cited first, 13 of 13)

- [Rapid training of Hamiltonian graph networks using random features](https://mlsanity.com/paper/2506.06558/) (2025)
- [HaM-World: Soft-Hamiltonian World Models with Selective Memory for Planning](https://mlsanity.com/paper/2605.05951/) (2026)
- [Controlled oscillation modeling using port-Hamiltonian neural networks](https://mlsanity.com/paper/2602.15704/) (2026)
- [Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics](https://mlsanity.com/paper/2604.00277/) (2026)
- [Unlocking the Invisible Urban Traffic Dynamics under Extreme Weather: A New Physics-Constrained Hamiltonian Learning Algorithm](https://mlsanity.com/paper/2512.03744/) (2025)
- [Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems](https://mlsanity.com/paper/2604.13297/) (2026)
- [Co-Learning Port-Hamiltonian Systems and Optimal Energy-Shaping Control](https://mlsanity.com/paper/2604.26172/) (2026)
- [Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equations](https://mlsanity.com/paper/2605.06246/) (2026)
- [Identifying the nonlinear string dynamics with port-Hamiltonian neural networks](https://mlsanity.com/paper/2605.12785/) (2026)
- [Latent Laplace Diffusion for Irregular Multivariate Time Series](https://mlsanity.com/paper/2605.19805/) (2026)
- [CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts](https://mlsanity.com/paper/2607.06824/) (2026)
- [Safe-by-Design Learning via Energy-based Neural Networks](https://mlsanity.com/paper/2609.36942/) (2026)
- [Port-Hamiltonian Neural Networks for Systems with Multiple Asymptotically Stable Equilibria](https://mlsanity.com/paper/2610.01356/) (2026)

## 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.