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

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.