MFEA-Net: A pixel-adaptive multigrid finite element analysis neural network for efficient material response prediction

Abstract

In this study, a novel physics-guided machine learning model, MFEA-Net, is proposed for the efficient prediction of mechanical responses in both single and multi-phase material systems. The MFEA-Net employs a data-driven Pixel-Adaptive Convolution (PAC) structure, unifying the modeling of arbitrary complex multi-phase systems. This is a significant enhancement for the finite element analysis neural networks (FEA-Net) that solve responses at the pixel level. Additionally, by integrating a geometric multigrid structure, the proposed model achieves ultra-fast convergence rates, substantially reducing the computational time required compared to conventional iterative methods. Smoothers for each grid level are refined using a three-layer convolutional neural network, innovatively adapted from the Jacobi smoother kernel to enhance performance. These modifications ensure excellent generalization capabilities and facilitate a computational algorithm characterized by linear time complexity. Several numerical experiments are performed to demonstrate and verify the proposed method with benchmark methods. The proposed MFEA-Net exhibits remarkable improvement in convergence efficiency over traditional Jacobi-based iteration methods, enabling it to predict material response 3-4 orders of magnitude faster.