Learning Stochastic Multiscale Models

2025/06/27 by Andrew F. Ilersich, Ilersich, Andrew F., Prasanth B. Nair +1 · 1 citation
Physics and Astronomy · Computer Science · #Model Reduction and Neural Networks #Advanced Mathematical Modeling in Engineering #Generative Adversarial Networks and Image Synthesis

paper · pdf · doi:10.48550/arxiv.2506.22655

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.

Citations

• Probabilistic Weather Forecasting with Hierarchical Graph Neural Networks
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• Problem reduction, renormalization, and memory

Cited by

• Why Does the Future Branch? Identifiable Closure Tests for Stochastic Physical World Models

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