Stable Port-Hamiltonian Neural Networks

TL;DR

This paper introduces stable port-Hamiltonian neural networks that embed physical principles to ensure stable, physically plausible, and robust learning of nonlinear dynamic systems, outperforming traditional data-driven models especially with limited data.

Contribution

It presents a novel neural network architecture that incorporates energy conservation and dissipation principles to guarantee global stability in learned dynamics.

Findings

Demonstrates robustness and stability in learning from sparse data

Outperforms purely data-driven models in accuracy and physical plausibility

Shows applicability to multi-physics simulation data

Abstract

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.