Nonlinear port-Hamiltonian system identification from input-state-output data

TL;DR

The paper develops a physics-guided method to identify nonlinear port-Hamiltonian systems from input-state-output data by learning state-dependent $J(x)$, $R(x)$, $B(x)$ and $H(x)$ with structure-preserving parametrizations. It compares MLPs and Kolmogorov-Arnold networks (KANs) for approximating the parameter functions, and introduces priors on the pH components to encode domain knowledge such as constant or quadratic Hamiltonians. Through three physical examples (mass-spring with nonlinear damping, magnetically levitated ball, and PMSM), the approach yields improved long-horizon predictions and data efficiency over baseline non-physics models, with priors further reducing data requirements. The work demonstrates robustness to noise and highlights that, in these settings, MLPs outperform KANs in both accuracy and training efficiency, while still preserving the energy-based structure that ensures passive behavior and stability.

Abstract

A framework for identifying nonlinear port-Hamiltonian systems using input-state-output data is introduced. The framework utilizes neural networks' universal approximation capacity to effectively represent complex dynamics in a structured way. We show that using the structure helps to make long-term predictions compared to baselines that do not incorporate physics. We also explore different architectures based on MLPs, KANs, and using prior information. The technique is validated through examples featuring nonlinearities in either the skew-symmetric terms, the dissipative terms, or the Hamiltonian.

Figures (10)

• Figure 1: Generic MLP or KAN architecture used for approximation of the parameter functions $\theta_{\bullet}$ where $\bullet\in\{J,B,R,H\}$.
• Figure 2: Average validation error for the spring model as a function of varying quantities of trajectories employed in training a baseline model, a default pH setup, and a pH setup incorporating prior knowledge.
• Figure 3: The trajectory of the momentum $p_2$ of the spring for different pH training setups. The vertical line at $10\,\mathrm{s}$ indicates the final time using in the training of the trajectories.
• Figure 4: Comparison between identified system parameters and true system parameters for changing state values $x$.
• Figure 5: NMAE in function of number of trajectories used for training for different priors for the spring example.