Learning Stochastic Reduced Models from Data: A Nonintrusive Approach

TL;DR

This paper introduces a nonintrusive data-driven method for creating reduced models of stochastic differential equations, accurately capturing statistical properties without intrusive system modifications.

Contribution

It develops a novel nonintrusive approach to infer reduced order models for stochastic systems, extending snapshot-based methods to stochastic cases and comparing with POD.

Findings

The proposed method accurately approximates statistical properties of high-dimensional stochastic systems.

Numerical experiments show comparable or improved performance over traditional POD methods.

The approach effectively generalizes snapshot-based subspace construction to stochastic differential equations.

Abstract

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive 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 generalisations of the snapshot-based dominant subspace construction to the stochastic case are presented. Numerical experiments are provided to compare the developed approach to POD.