Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems

2025-08-17

AI Summary

This work addresses the challenge of learning physically consistent coarse-grained dynamics from particle trajectory time series in nonequilibrium multiscale systems. We propose a structure-preserving modeling paradigm grounded in the metriplectic bracket, rigorously enforcing the first and second laws of thermodynamics, momentum conservation, and the fluctuation–dissipation relation under discrete-time evolution. A self-supervised learning strategy is introduced to implicitly identify entropy-related structural variables, thereby capturing memory effects and stochasticity. The method integrates deep learning with molecular dynamics (open-source implementations in PyTorch and LAMMPS) to enable efficient large-scale inference. Validated on video data of star polymers and colloidal suspensions, our approach achieves over 100× coarse-graining while accurately reproducing nonequilibrium statistical properties, local rearrangements, and the coupling between macroscopic stochastic dynamics and microstructural evolution—substantially outperforming conventional black-box models.

Technology Category

• Machine Learning: Structured Learning
• Search and Optimization: Learning to Search
• Multiagent Systems: Multiagent Learning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

Problem

• Linking short scales to emergent bulk physics in multiscale systems
• Preserving thermodynamic laws in coarse-grained particle dynamics
• Learning entropic state variables without labels for non-equilibrium systems

Innovation

• Metriplectic bracket formalism for dynamics
• Self-supervised learning for variables
• Open-source PyTorch and LAMMPS implementation