A multigrid finite element neural network for efficient material response prediction

A multigrid data-driven model is proposed to efficiently predict the mechanical response of single/multi-phase materials. The model uses a finite element analysis neural network (FEANet) to iteratively solve the response at a grid level. The efficiency is achieved by applying the intergrid communication and smoothing operators between grids in a predefined hierarchy. Current work is based on the geometric multigrid methods, since the grid hierarchy is fixed. However the inter-grid operators and smoothers are learned from neural networks. The inter-grid operators, i.e., prolongation kernels, are learned from a encoder-decoder convolutional network. The smoothers are modified based on the Jacobi smoother kernel, and the modification is learned from a three-layer convolutional neural network. The learned prolongation operators and smoothers have good generalization properties and result in a computational algorithm with linear time complexity. The proposed methodology is shown to outperform the simple Jacobi-based multigrid method in terms of convergence rate and interface error reduction. A multigrid data-driven model is proposed to efficiently predict the mechanical response of single/multi-phase materials. The model uses a finite element analysis neural network (FEANet) to iteratively solve the response at a grid level. The efficiency is achieved by applying the intergrid communication and smoothing operators between grids in a predefined hierarchy. Current work is based on the geometric multigrid methods, since the grid hierarchy is fixed. However the inter-grid operators and smoothers are learned from neural networks. The inter-grid operators, i.e., prolongation kernels, are learned from a encoder-decoder convolutional network. The smoothers are modified based on the Jacobi smoother kernel, and the modification is learned from a three-layer convolutional neural network. The learned prolongation operators and smoothers have good generalization properties and result in a computational algorithm with linear time complexity. The proposed methodology is shown to outperform the simple Jacobi-based multigrid method in terms of convergence rate and interface error reduction.