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

TL;DR

PEGNet tackles the challenge of long-term stability and physical consistency in data-driven multiphysics PDE simulations by embedding physics through PDE-guided message passing. The framework uses an Encode-Process-Decode architecture with a Physics-Guided Message Passing module consisting of Navier-Stokes (NS) and Advection-Diffusion (AD) blocks to respect governing equations while operating on a multi-scale graph. It introduces physics-informed losses and a bi-stride pooling strategy, and demonstrates superior long-term accuracy and physical consistency across cylinder flow, 3D airflow in airways, and drug delivery simulations, with generalization to Gray-Scott reaction-diffusion. The results indicate PEGNet outperforms strong baselines in both predictive accuracy and adherence to physical constraints, offering a scalable, differentiable tool for fast multiphysics simulations in irregular geometries. This work has practical impact for medical physics applications and optimization of therapies, while future work will address more realistic 3D anatomies and Lagrangian formulations to further enhance applicability.

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.

Figures (12)

• Figure 1: (a) The overall framework of PEGNet. (b) The internal structure of the PGMP module, which consists of a one-way coupled NS Block and AD Block. (c) A detailed view of the internal structures of the NS Block and AD Block, showing how PDE-guided message passing is implemented.
• Figure 2: Multi-Task Adaptability of PGMP. The component within the red box can be omitted for single-phase flow, or extended to predict multiple scalar fields.
• Figure 3: Overview of respiratory simulation datasets generated by traditional numerical methods: (a) Partial view of the human airway. (b) Streamlines of inhaled airflow in the upper respiratory tract, showing complex flow with backflow and vortices. (c) Cross-section at the lower tract bifurcation, colored by speed magnitude with contour lines. (d) Cross-section of the upper tract with a mouthpiece, colored by concentration magnitude with contour lines.
• Figure 4: From $t=0$ to $t=800$ represents a complete inhalation-exhalation cycle, with key points at $t=0$ (start of inhalation), $t=200$ (peak inhalation velocity), $t=400$ (start of exhalation), $t=600$ (peak exhalation velocity), and $t=800$ (end of exhalation). The BSMS-GNN model shows increasing artifacts in the central airway, predicting airflow even after exhalation ends, contrary to reality. In contrast, our model remains more stable with only minor artifacts near the cycle's end.
• Figure A.1: (a) Simplification of human airways, which are used for the airflow simulation. (b) Upper airway model for drug delivery simulation. Unlike the model used in the airflow simulation, this simulation adds a mouthpiece in front of the oral cavity to simulate the entry of drugs and airflow into the mouth via a specific device.