SPIEDiff: robust learning of long-time macroscopic dynamics from short-time particle simulations with quantified epistemic uncertainty

TL;DR

SPIEDiff is a machine learning framework that accurately predicts long-time macroscopic dynamics and thermodynamics of dissipative systems from short-time particle simulations, with quantified uncertainty and reduced computational cost.

Contribution

It introduces SPIEDiff, a novel physics-informed diffusion model that overcomes time-scale limitations and uncertainty quantification challenges in data-driven thermodynamic discovery.

Findings

Accurately uncovers thermodynamics and kinetics from short-time data

Provides reliable long-time predictions with quantified uncertainty

Reduces computational time from days/years to minutes

Abstract

The data-driven discovery of long-time macroscopic dynamics and thermodynamics of dissipative systems with particle fidelity is hampered by significant obstacles. These include the strong time-scale limitations inherent to particle simulations, the non-uniqueness of the thermodynamic potentials and operators from given macroscopic dynamics, and the need for efficient uncertainty quantification. This paper introduces Statistical-Physics Informed Epistemic Diffusion Models (SPIEDiff), a machine learning framework designed to overcome these limitations in the context of purely dissipative systems by leveraging statistical physics, conditional diffusion models, and epinets. We evaluate the proposed framework on stochastic Arrhenius particle processes and demonstrate that SPIEDiff can accurately uncover both thermodynamics and kinetics, while enabling reliable long-time macroscopic predictions using only short-time particle simulation data. SPIEDiff can deliver accurate predictions with quantified uncertainty in minutes, drastically reducing the computational demand compared to direct particle simulations, which would take days or years in the examples considered. Overall, SPIEDiff offers a robust and trustworthy pathway for the data-driven discovery of thermodynamic models.