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

TL;DR

The paper introduces a metriplectic/GENERIC-based, structure-preserving framework to learn coarse-grained, stochastic particle dynamics from trajectory data while enforcing discrete thermodynamic laws. It provides parameterizations for energy, entropy, and noise that guarantee detailed fluctuation-dissipation balance and momentum conservation, supplemented by a self-supervised entropy variable discovery. Across ideal gas, star-polymer coarse-graining, viscoelastic solids, and jammed colloids, the method preserves non-equilibrium statistics and outperforms standard GNN-based coarse-graining and DPD baselines, with scalable implementations in PyTorch and LAMMPS. The work demonstrates broad applicability and scalability, including weak scaling to millions of particles, and outlines extensions to new physics and architectures for further improvements.

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.

Figures (13)

• Figure 1: Exemplar applications using data-driven particle dynamics to bridge scales in simulated (top) and experimental (bottom) datasets. (A) Detailed simulation of polymers fully resolve stochastic fluctuations (left), in-silico experiments of a small domain supervise model discovery (middle), yielding a data-driven model for non-equilibrium bulk response solved in a massive parallel simulator (right). (B) A 2D suspension in an oscillatory shear flow provides a rich multiphysics/multiscale exemplar incorporating lubrication, electrostatics, contact, and stochasticity (left). Trajectories of particle data are extracted using computer vision techniques, providing complete top-down (but noisy) data to supervise model collection (center), ultimately yielding a model which predicts linkages between structure and emergent dynamics (right).
• Figure 2: Ideal Gas datasets. Flow configurations for (A) Taylor-Green training dataset, and (B) Self Diffusion and (C) Shear Flow testing datasets. We confirm generalization of non-equilibrium statistics in (B) and (C) despite distinct flow conditions held out during training.
• Figure 3: Representative star polymers coarse grained into a single data-driven particle in Star Polymer datasets. (A) Star Polymer 11 with 1 core, 10 arms and 1 bead per arm. (B) Star Polymer 51 with 1 core, 10 arms and 5 beads per arm.
• Figure 4: Correlation metrics for the (A) Star polymer 11 and (B) Star polymer 51 datasets, establishing recovery of structure and dissipative response. Other deep learning baselines (GNS, GNS-SDE) fail to recover structural or dynamical statistics and produce unstable results (outside the plotting range). In contrast, a classical model such as DPD captures some dynamical information but inaccurately.
• Figure 5: Computation time required for a fixed number of CPUs per processor without GPU acceleration. A flat curve denotes weak scaling, demonstrating that systems of arbitrary size may be considered by scaling CPUs proportional to numbers of particles.

Theorems & Definitions (18)

• Proposition 5.1
• proof
• Proposition 5.2
• proof
• Proposition 5.3
• proof
• Lemma A.1
• proof
• Proposition B.1
• proof