PEGNet: A Physics-Embedded Graph Network for Long-Term Stable Multiphysics Simulation

TL;DR

PEGNet is a novel graph neural network that embeds PDE physics into its architecture, enabling stable, accurate, and physically consistent long-term simulations of complex multiphysics phenomena.

Contribution

The paper introduces PEGNet, a physics-embedded graph network that incorporates PDE-guided message passing and hierarchical features for improved multiphysics simulation stability and accuracy.

Findings

Outperforms existing methods in long-term stability.

Achieves higher physical consistency in simulations.

Demonstrates effectiveness on respiratory airflow and drug delivery datasets.

Abstract

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often computationally expensive. Recently, data-driven methods have emerged as alternatives, but they frequently suffer from error accumulation and limited physical consistency, especially in multiphysics and complex geometries. To address these challenges, we propose PEGNet, a Physics-Embedded Graph Network that incorporates PDE-guided message passing to redesign the graph neural network architecture. By embedding key PDE dynamics like convection, viscosity, and diffusion into distinct message functions, the model naturally integrates physical constraints into its forward propagation, producing more stable and physically consistent solutions. Additionally, a hierarchical architecture is employed to capture multi-scale features, and physical regularization is integrated into the loss function to further enforce adherence to governing physics. We evaluated PEGNet on benchmarks, including custom datasets for respiratory airflow and drug delivery, showing significant improvements in long-term prediction accuracy and physical consistency over existing methods. Our code is available at https://github.com/Yanghuoshan/PEGNet.