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Data-driven particle dynamics: Structure-preserving coarse-graining for emergent behavior in nonequilibrium systems.

Quercus Hernández1, Max Win1, Thomas C O'Connor2

  • 1Department of Mechanical Engineering and Applied Mechanics, School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104.

Proceedings of the National Academy of Sciences of the United States of America
|May 13, 2026
PubMed
Summary

We developed a machine learning framework to simulate complex multiscale systems by preserving thermodynamic laws and physical properties. This approach accurately models coarse-grained dynamics from particle trajectory data, even without labels.

Keywords:
coarse-grainingdata-driven modelingmachine learningmultiscale systemssoft matter

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Published on: February 22, 2018

Area of Science:

  • Computational Physics
  • Machine Learning
  • Statistical Mechanics

Background:

  • Multiscale systems simulation is challenging due to linking short spatiotemporal scales to emergent bulk physics.
  • Coarse-graining dynamical systems leads to entropic information loss, resulting in dissipative, history-dependent, and stochastic emergent physics.
  • Existing methods struggle to preserve fundamental physical properties during coarse-graining.

Purpose of the Study:

  • To propose a novel machine learning framework for learning coarse-grained dynamics from particle trajectory data.
  • To develop a method that preserves key physical properties like thermodynamic laws and fluctuation-dissipation balance during coarse-graining.
  • To enable accurate simulation of complex multiscale systems by machine learning emergent behaviors.

Main Methods:

  • Utilized the metriplectic bracket formalism to construct a machine learning framework.
  • Developed a self-supervised learning strategy to identify emergent structural variables without explicit labels.
  • Applied particle discretization to specialize the mathematical framework for trajectory data.

Main Results:

  • The framework guarantees discrete conservation laws (thermodynamics, momentum) and fluctuation-dissipation balance.
  • Successfully validated on benchmark systems and demonstrated on coarse-graining star polymers and colloidal suspensions.
  • Captured nonequilibrium statistics and coupling between local events and emergent stochastic dynamics in complex systems.

Conclusions:

  • The proposed framework offers a robust method for machine learning coarse-grained dynamics while preserving essential physical laws.
  • Enables accurate simulation of complex multiscale phenomena, particularly in nonequilibrium statistical mechanics.
  • Provides open-source implementations (PyTorch, LAMMPS) for broad applicability and extensibility to diverse particle-based systems.