Structure- and Stability-Preserving Learning of Port-Hamiltonian Systems
For researchers in data-driven modeling of physical systems, this work offers a more flexible and accurate approach to preserving Hamiltonian structure and stability, though it is incremental over existing neural-network-based methods.
This paper proposes a neural-network-based method for learning port-Hamiltonian systems that removes the convexity constraint on Hamiltonian approximations, improving expressiveness and generalization, and preserves stability of multiple isolated equilibria. Numerical experiments show more accurate structure- and stability-preserving learning compared to a baseline method.
This paper investigates the problem of data-driven modeling of port-Hamiltonian systems while preserving their intrinsic Hamiltonian structure and stability properties. We propose a novel neural-network-based port-Hamiltonian modeling technique that relaxes the convexity constraint commonly imposed by neural network-based Hamiltonian approximations, thereby improving the expressiveness and generalization capability of the model. By removing this restriction, the proposed approach enables the use of more general non-convex Hamiltonian representations to enhance modeling flexibility and accuracy. Furthermore, the proposed method incorporates information about stable equilibria into the learning process, allowing the learned model to preserve the stability of multiple isolated equilibria rather than being restricted to a single equilibrium as in conventional methods. Two numerical experiments are conducted to validate the effectiveness of the proposed approach and demonstrate its ability to achieve more accurate structure- and stability-preserving learning of port-Hamiltonian systems compared with a baseline method.