Physics-informed random neural architectures on compact boundaryless multiply connected manifolds for random-operator models in machine learning and uncertainty quantification

We introduce stochastic physics-informed neural networks (SPINNs) for stochastic boundary-value problems (SBVPs) with random operators. The method enforces physics through a structural probabilistic coupling: a common Gaussian stochastic germ drives both the SBVP random operator and a manifold-based