Stochastic physics-informed neural networks with random architectures on manifolds for surrogate modeling of random input-output operators: structural distinctions from conventional neural networks
Year: 2026
Type: other
Abstract: The stochastic physics-informed neural network (SPINN) formulation developed by Soize (2027, Physics-informed random neural architectures on compact boundaryless multiply connected manifolds for random-operator models in machine learning and uncertainty quantification) differs structurally from conventional artificial neural networks used in physics-informed learning. Its neural architecture is generated probabilistically on a compact, boundaryless, multiply connected manifold, rather than prescribed as a fixed feedforward network. A common Gaussian stochastic germ couples its latent neural structure to the random operator of a stochastic boundary-value problem. Calibration then combines observation likelihood and an alignment of conditional probability distributions, without differential-equation residual penalties. This note identifies these distinct mechanisms, clarifies their scientific attribution, and summarizes the scope of the numerical evidence. It introduces no additional theoretical or numerical results.
Source: HAL
Author: Christian Soize
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225126157