Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees
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 Itô dynamics we establish a weak passivity inequality in expectation under an explicit generator condition, stated for a stopped process on a compact set. We also prove a universal approximation result showing that, on any compact set and finite horizon, SPH-NNs approximate the coefficients of a target stoc...
| Authors | Luca Di Persio, Matthias Ehrhardt, Youness Outaleb |
|---|---|
| Primary category | cs.LG |
| Published | 10 March 2026 |
| Last updated at source | 10 March 2026 |
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