A Comprehensive Evaluation of Graph Neural Networks and Physics Informed Learning for Surrogate Modelling of Finite Element Analysis

Abstract

Although Finite Element Analysis (FEA) is an integral part of the product design lifecycle, the analysis is computationally expensive, making it unsuitable for many design optimization problems. The deep learning models can be a great solution. However, selecting the architecture that emulates the FEA with great accuracy is a challenge. This paper presents a comprehensive evaluation of graph neural networks (GNNs) and 3D U-Nets as surrogates for FEA of parametric I-beams. We introduce a Physics-Informed Neural Network (PINN) framework, governed by the Navier Cauchy equations, to enforce physical laws. Crucially, we demonstrate that a curriculum learning strategy, pretraining on data followed by physics informed fine tuning, is essential for stabilizing training. Our results show that GNNs fundamentally outperform the U-Net. Even the worst performer among GNNs, the GCN framework, achieved a relative L2 error of 8.7% while the best framework among U Net, U Net with attention mechanism trained on high resolution data, achieved 13.0% score. Among the graph-based architectures, the Message Passing Neural Networks (MPNN) and Graph Transformers achieved the highest accuracy, achieving a relative L2 score of 3.5% and 2.6% respectively. The inclusion of physics fundamental laws (PINN) significantly improved the generalization, reducing error by up to 11.3% on high-signal tasks. While the Graph Transformer is the most accurate model, it is more 37.5% slower during inference when compared to second best model, MPNN PINN. The PINN enhanced MPNN (MPNN PINN) provides the most practical solution. It offers a good compromise between predictive performance, model size, and inference speed.