A non-intrusive 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.

翻译：本文针对具有加性噪声的双线性随机微分方程，提出了一种非侵入式模型降阶方法。所设计的降阶模型旨在近似高维系统的统计特性。通过求解适当的最小二乘问题，从状态观测数据中推断出降阶模型的漂移系数与扩散系数。本文研究了所提方法获得的降阶模型与通过本征正交分解方法获得的侵入式降阶模型之间的逼近程度。提出了基于快照的主导子空间构造在随机情形下的两种推广形式，并通过数值实验将所发展的方法与POD方法进行了比较。