Stable Port-Hamiltonian Neural Networks (2502.02480v1)

Abstract: In recent years, nonlinear dynamic system identification using artificial neural networks has garnered attention due to its manifold potential applications in virtually all branches of 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 proposes stable port-Hamiltonian neural networks, a machine learning architecture that incorporates the physical biases of energy conservation or dissipation while guaranteeing global Lyapunov stability of the learned dynamics. Evaluations with illustrative examples and real-world measurement data demonstrate the model's ability to generalize from sparse data, outperforming purely data-driven approaches and avoiding instability issues. In addition, the model's potential for data-driven surrogate modeling is highlighted in application to multi-physics simulation data.