Stochastic Port-Hamiltonian Neural Networks: Universal Approximation with Passivity Guarantees

2026-03-10

AI Summary

This work proposes the first stochastic port-Hamiltonian neural network with passivity guarantees for open stochastic dynamical systems subject to dissipation, external inputs, and stochastic disturbances. The approach parameterizes the Hamiltonian via a neural network and enforces structural constraints—namely, skew-symmetry of the interconnection matrix and positive semi-definiteness of the dissipation matrix—to ensure compliance with the stochastic port-Hamiltonian form. Within the Itô framework, a weak passivity inequality is established in expectation. Theoretically, the model is shown to possess universal approximation capability with C² accuracy over compact sets and exhibits mean-square convergence of solution trajectories. Experimental results on noisy mass-spring, Duffing, and Van der Pol oscillator systems demonstrate that the proposed method significantly improves long-horizon roll-out prediction accuracy and reduces energy errors compared to standard MLP baselines.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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. We also prove a universal approximation result showing that, on any compact set and finite horizon, SPH-NNs approximate the coefficients of a target stochastic port-Hamiltonian system with $C^2$ accuracy of the Hamiltonian and yield coupled solutions that remain close in mean square up to the exit time. Experiments on noisy mass spring, Duffing, and Van der Pol oscillators show improved long horizon rollouts and reduced energy error relative to a multilayer perceptron baseline.

Problem

• stochastic port-Hamiltonian systems
• passivity
• universal approximation
• energy-based modeling
• stochastic dynamics

Innovation

• Stochastic Port-Hamiltonian Systems
• Neural Networks
• Passivity
• Universal Approximation
• Structure-Preserving Learning