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

Multiscale systems are common in science and engineering but remain difficult to simulate, as fine spatiotemporal scales must be consistently linked to emergent bulk behavior. Coarse-graining high-dimensional dynamics into low-dimensional models causes entropic information loss, producing dissipative, history-dependent, and stochastic effects. We present a metriplectic bracket based framework for learning coarse-grained dynamics from particle-trajectory time series, which enforces by construction the first and second laws of thermodynamics, momentum conservation, and discrete fluctuation–dissipation balance, crucial for capturing non-equilibrium statistics. After introducing the formalism, we specialize it to particle discretizations and develop a self-supervised strategy to recover unobserved entropic state variables. The method is applied to: (i) coarse-graining star polymers at extreme resolutions while retaining non-equilibrium statistics, and (ii) learning from high-speed video of colloidal suspensions to capture coupling between local rearrangements and emergent stochasticity. Our open-source PyTorch and LAMMPS implementations enable large-scale inference and extension to diverse particle-based systems.