Scalable learning of macroscopic stochastic dynamics

TL;DR

This paper introduces a scalable machine learning framework that learns macroscopic stochastic dynamics from small-system simulations, enabling efficient modeling of large complex systems without extensive computational resources.

Contribution

It proposes a novel partial evolution and hierarchical upsampling scheme to accurately learn large-system macroscopic behavior from limited small-system data.

Findings

Framework accurately models stochastic systems like SPDEs and lattice spins.

Demonstrates robustness across diverse physical systems.

Enables efficient large-system simulation from small-system data.

Abstract

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to first-principles methods to build accurate macroscopic models from microscopic trajectory simulations. However, for spatially extended systems, direct simulations of sufficiently large microscopic systems that inform macroscopic behavior is prohibitive. In this work, we propose a framework that learns the macroscopic dynamics of large stochastic microscopic systems using only small-system simulations. Our framework employs a partial evolution scheme to generate training data pairs by evolving large-system snapshots within local patches. We subsequently identify the closure variables associated with the macroscopic observables and learn the macroscopic dynamics using a custom loss. Furthermore, we introduce a hierarchical upsampling scheme that enables efficient generation of large-system snapshots from small-system trajectory distributions. We empirically demonstrate the accuracy and robustness of our framework through a variety of stochastic spatially extended systems, including those described by stochastic partial differential equations, idealised lattice spin systems, and a more realistic NbMoTa alloy system.