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 stochastic neural architecture. The stochastic neural network is non-feedforward and intrinsically random. A latent Gaussian field and an inhomogeneous Poisson point process on a compact, boundaryless, multiply connected manifold generate random neuron locations, geodesically local sparse connectivity, and a sparse random weight matrix, all governed by a low-dimensional hyperparameter. For det...
| Authors | Christian Soize |
|---|---|
| Primary category | stat.ML |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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