  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.
