Learning Stochastic Multiscale Models

2025-06-27

AI Summary

Modeling multiscale dynamical systems faces challenges from high-dimensional state spaces and difficult characterization of cross-scale couplings. This paper proposes a data-driven coarse-graining paradigm: it directly learns stochastic differential equation (SDE) models with auxiliary states from observational data, explicitly representing unresolved-scale effects on a low-dimensional grid. The method integrates physical priors with amortized variational inference, enabling efficient parameter learning without requiring forward solvers. Experiments demonstrate that the proposed model significantly outperforms both direct numerical simulation and conventional closure models at identical resolution—achieving markedly improved predictive accuracy. The approach offers a new modeling pathway for complex multiscale systems that is interpretable, scalable, and computationally efficient.

Technology Category

• Machine Learning: Multimodal Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

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.

Problem

• Learning stochastic multiscale models from observational data
• Resolving coarse mesh states with auxiliary unresolved scale effects
• Improving predictive accuracy over direct numerical simulation

Innovation

• Learning stochastic multiscale models from data
• Using coarse mesh with auxiliary state
• Forward-solver-free amortized variational inference