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

2025-11-11

AI Summary

Traditional PDE solvers suffer from high computational cost, while existing data-driven methods exhibit error accumulation and physical inconsistency in multi-physics and complex-geometry settings. To address these challenges, we propose a PDE-guided graph neural network architecture. Our method decomposes physical processes—including advection, viscosity, and diffusion—into distinct message-passing functions, and integrates multi-scale feature extraction with physics-informed regularization losses through mechanism-driven decomposition and hierarchical architectural design. This enhances long-term stability and conservation properties. Evaluated on multi-physics simulation tasks—such as respiratory airflow and aerosol drug delivery—our approach achieves higher prediction accuracy and stronger physical consistency compared to state-of-the-art models. It establishes a new paradigm for long-term, stable, and physically faithful simulation on complex geometries.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Computer Vision: Low Level & Physics-based Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

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.

Problem

• Addresses error accumulation in data-driven multiphysics simulations
• Improves physical consistency in complex geometry PDE solutions
• Enhances long-term stability for convection-diffusion system predictions

Innovation

• Physics-embedded graph network redesigns architecture
• Hierarchical architecture captures multi-scale physical features
• Physical regularization enforces adherence to governing physics