Scalable learning of macroscopic stochastic dynamics

2025-11-16

AI Summary

To address the prohibitive computational cost of direct simulation in macroscopic modeling of large-scale stochastic microscopic systems, this paper proposes a novel paradigm for learning macroscopic closure equations directly from fine-scale trajectory data. Methodologically, we design a local block-evolution sampling strategy to generate training data and develop a deep learning framework integrating statistical inference with multiscale modeling. Innovatively, we introduce a hierarchical upsampling mechanism and a customized loss function to automatically identify effective macroscopic variables and learn their dynamical closures. The method is validated across diverse spatially extended systems—including stochastic partial differential equations, lattice spin models, and the NbMoTa alloy—demonstrating substantial reductions in computational overhead while preserving macroscopic prediction accuracy and cross-scale robustness.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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.

Problem

• Learning macroscopic dynamics from small stochastic system simulations
• Developing scalable framework for large spatially extended systems
• Addressing computational cost of direct large microscopic simulations

Innovation

• Learning macroscopic dynamics from small-system simulations
• Employing partial evolution scheme for training data
• Hierarchical upsampling for large-system snapshot generation