Multifidelity graph neural networks for efficient and accurate mesh‐based partial differential equations surrogate modeling

Abstract

Accurately predicting the dynamics of complex systems governed by partial differential equations (PDEs) is crucial in various applications. Traditional numerical methods such as finite element methods (FEMs) offer precision but are resource-intensive, particularly at high mesh resolutions. Machine learning–based surrogate models, including graph neural networks (GNNs), present viable alternatives by reducing computation times. However, their accuracy is significantly contingent on the availability of substantial high-fidelity training data. This paper presents innovative multifidelity GNN (MFGNN) frameworks that efficiently combine low-fidelity and high-fidelity data to train more accurate surrogate models for mesh-based PDE simulations, while reducing training computational cost. The proposed methods capitalize on the strengths of GNNs to manage complex geometries across different fidelity levels. Incorporating a hierarchical learning strategy and curriculum learning techniques, the proposed models significantly reduce computational demands and improve the robustness and generalizability of the results. Extensive validations across various simulation tasks show that the MFGNN frameworks surpass traditional single-fidelity GNN models. The proposed approaches, hence, provide a scalable and practical solution for conducting detailed computational analyses where traditional high-fidelity simulations are time-consuming.