  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.
