Comparing model representations and fitting methods for port-Hamiltonian system identification

Port-Hamiltonian models describe physical systems by separating stored energy, dissipation and external inputs. Learning such models from data requires a choice of representation and fitting method. We compare using neural networks, analytic expressions and combinations of the two for representing the different components of the port-Hamiltonian system, and compare fitting the models with gradient-based optimisation or sparse regression. Testing on simulations of mechanical and electrical systems, with and without added noise, we present prediction accuracy and computational cost of the different approaches.