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arXiv · 2508.12569

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

Quercus Hernandez·Max Win·Thomas C. O'Connor·Paulo E. Arratia·Nathaniel Trask
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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.

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Quercus Hernandez, Max Win, Thomas C. O'Connor, Paulo E. Arratia, Nathaniel Trask. 2025-12-29. Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems. https://arxiv.org/abs/2508.12569

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