Integrating Port-Hamiltonian Systems with Neural Networks: From Deterministic to Stochastic Frameworks

Abstract: This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and computational models that extend the understanding of dynamical systems under uncertainty and complex interactions. It emphasizes the significant progress in learning and predicting the dynamics of non-autonomous systems using port-Hamiltonian neural networks (pHNNs). It also explores the implications of stochastic neural networks in various dynamical systems.