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

• URL: http://arxiv.org/abs/2508.12569v1
• Date: Mon, 18 Aug 2025 02:10:18 GMT
• Title: Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in non-equilibrium systems
• Authors: Quercus Hernandez, Max Win, Thomas C. O'Connor, Paulo E. Arratia, Nathaniel Trask,
• Abstract summary: Multiscale systems are notoriously challenging to simulate as shorttemporal scales must be appropriately linked to emergent bulk physics.<n>We propose a framework using the metriplectic bracket formalism that preserves discrete notions of the first and second laws of thermodynamics.<n>We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and rearrangement to diverse particle-based systems.
• Score: 0.8796261172196743
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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