Learning Stochastic Multiscale Models
This addresses computational bottlenecks in physical sciences for researchers and engineers dealing with multiscale systems, though it is incremental as it builds on physics-based modeling approaches.
The paper tackles the computational challenge of simulating dynamical systems with wide-ranging scales by learning stochastic multiscale models from data, achieving superior predictive accuracy compared to existing methods like under-resolved simulations and closure models.
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. Drawing inspiration from physics-based multiscale modeling approaches, we resolve the macroscale state on a coarse mesh while introducing a microscale latent state to explicitly model unresolved dynamics. We learn the parameters of the multiscale model using a simulator-free amortized variational inference method with a Product of Experts likelihood that enforces scale separation. We present detailed numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy compared to under-resolved direct numerical simulation and closure-type models at equivalent resolution, as well as reduced-order modeling approaches.