Learning Stochastic Multiscale Models

Abstract: The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at the finest relevant scales, leading to a high-dimensional state space. In this work, we propose an approach to learn stochastic multiscale models in the form of stochastic differential equations directly from observational data. Our method resolves the state on a coarse mesh while introducing an auxiliary state to capture the effects of unresolved scales. We learn the parameters of the multiscale model using a modern forward-solver-free amortized variational inference method. Our approach draws inspiration from physics-based multiscale modeling approaches, such as large-eddy simulation in fluid dynamics, while learning directly from data. We present numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy compared to direct numerical simulation and closure-type models at equivalent resolution.