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

TL;DR

This paper presents a neural network-based framework for identifying nonlinear port-Hamiltonian systems from input-state-output data, leveraging structure to improve long-term prediction accuracy and incorporating various architectures and prior information.

Contribution

The paper introduces a structured neural network approach for nonlinear port-Hamiltonian system identification that enhances prediction accuracy by embedding physical structure.

Findings

Structure-aware models outperform unstructured baselines in long-term predictions.

Different neural network architectures can effectively model various nonlinearities.

Incorporating prior information improves model fidelity.

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.