Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees
arXiv:2603.10078v1 Announce Type: new Abstract: Stochastic port-Hamiltonian systems represent open dynamical systems with dissipation, inputs, and stochastic forcing in an energy based form. We introduce stochastic port-Hamiltonian neural networks, SPH-NNs, which parameterize the Hamiltonian with a feedforward network and enforce skew symmetry of the interconnection matrix and positive semidefiniteness of the dissipation matrix. For It^o dynamics we establish a weak passivity inequality in expectation under an explicit generator condition, stated for a stopped process on a compact set. […]