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

TL;DR

This paper presents a physics-informed machine learning framework for coarse-graining multiscale particle systems, preserving thermodynamic laws and non-equilibrium behavior, validated on complex polymer and colloidal systems.

Contribution

It introduces a novel structure-preserving learning approach using the metriplectic bracket formalism, with a self-supervised method for identifying emergent variables from trajectory data.

Findings

Successfully coarse-grained star polymers while maintaining non-equilibrium statistics.

Learned models from high-speed video capturing stochastic dynamics in colloids.

Open-source tools facilitate large-scale inference in particle systems.

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.