Learning Stochastic Reduced Models from Data: A Nonintrusive Approach

.A nonintrusive model order reduction method for bilinear stochastic differential equations with additive Gaussian noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional systems. The drift and diffusion coefficients of the ROM are inferred from state observations by solving appropriate least-squares problems. The closeness of the ROM obtained by the presented approach to the intrusive ROM obtained by the proper orthogonal decomposition (POD) method is investigated. Two generalizations of the snapshot-based dominant subspace construction to the stochastic case are presented. Numerical experiments are provided to compare the developed approach to POD.Reproducibility of computational results.This paper has been awarded the "SIAM Reproducibility Badge: Code and data available" as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/JMNicolaus/OperatorInference_for_SDEs and in the supplementary materials (OperatorInference_for_SDEs-main.zip [73.5KB]).Keywordsnonintrusive model reductiondata-driven modelingoperator learningscientific machine learningstochastic systemsMSC codes60H1060H3565C3060G51