Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations

TL;DR

This paper introduces a hybrid physics-neural model that accelerates complex 3D scalar transport simulations by orders of magnitude, using a differentiable framework to learn physical parameters and non-Markovian closures for stable, long-term predictions.

Contribution

The work presents a novel differentiable physics-neural approach that jointly learns physical parameters and non-Markovian neural closures for efficient, accurate coarse-grained simulations.

Findings

Achieves simulation speedup from hours to under 1 minute.

Maintains high correlation (0.96 Spearman) in out-of-distribution scenarios.

Requires only 26 training data points for effective learning.

Abstract

Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This work presents a hybrid physics-neural model that predicts scalar transport in a complex domain orders of magnitude faster than the 3D simulation (from hours to less than 1 min). This end-to-end differentiable framework jointly learns the physical model parameterization (i.e. orthotropic diffusivity) and a non-Markovian neural closure model to capture unresolved, 'coarse-grained' effects, thereby enabling stable, long time horizon rollouts. This proposed model is data-efficient (learning with 26 training data), and can be flexibly extended to an out-of-distribution scenario (with a moving source), achieving a Spearman correlation coefficient of 0.96 at the final simulation time. Overall results show that this differentiable physics-neural framework enables fast, accurate, and generalizable coarse-grained surrogates for physical phenomena.