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

2025-11-26

AI Summary

Addressing the challenge of computationally expensive (hour-scale) and poorly generalizable scalar transport simulation in complex physical domains, this paper proposes an end-to-end differentiable physics–neural hybrid model. Methodologically, it integrates an anisotropic diffusion equation with a non-Markovian neural closure term to construct a coarse-grained surrogate model, jointly optimizing both physical parameters and the neural module via a differentiable simulator. The key contribution lies in the first incorporation of a non-Markovian architecture into a differentiable physics-based framework, enabling stable long-term forecasting and strong out-of-distribution (OOD) generalization. With only 26 training samples, the model achieves a Spearman correlation coefficient of 0.96 at the final time step. It maintains high accuracy even under OOD scenarios—such as moving pollution sources—and reduces computational cost from hours to minutes.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Mixture of Experts (MoE)

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

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.

Problem

• Learning non-Markovian closures for accelerated coarse-grained physics simulations
• Predicting scalar transport faster than 3D simulations using hybrid models
• Developing data-efficient differentiable frameworks for physical phenomena surrogates

Innovation

• Hybrid physics-neural model for scalar transport
• Learns orthotropic diffusivity and neural closure model
• Enables stable long time horizon rollouts