Learning Stochastic Multiscale Models

• URL: http://arxiv.org/abs/2506.22655v2
• Date: Fri, 07 Nov 2025 23:02:26 GMT
• Title: Learning Stochastic Multiscale Models
• Authors: Andrew F. Ilersich, Prasanth B. Nair,
• Abstract summary: We learn multiscale models in the form of differential equations directly from observational data.<n>We learn the parameters of the multiscale model using a simulator-free amortized variational inference method.<n>We present detailed numerical studies to demonstrate that our learned multiscale models achieve superior predictive accuracy.
• Score: 2.005299372367689
• License: http://creativecommons.org/licenses/by/4.0/
• 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. 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.

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