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

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.