How to achieve the fast computation for voxel-based irregular structures by few finite elements?

Abstract

We propose machine learning (ML) based smart interpolation functions to enhance the finite element computation (named as smart-I finite element) for the heterogeneous structures (e.g., alloy material, concrete material and porous rock) that is composed of many microstructures known as voxel-based irregular shape (VI-shape). This element can directly describe the geometries with different VI-shapes and material properties without the complex meshing process by traditional finite element method (FEM). To achieve the smart interpolation in such element, a machine learning algorithm containing multiple parallel artificial neural networks (ANNs) and DeepONets assembled by the convolutional architectures is constructed for the fast prediction of interpolation functions. On this basis, the smart-I finite element is combined with classic FEM element to derive the global equilibrium equations and obtain the full-field variable distribution. Numerical tests with various material, geometrical as well as loading parameters prove that, the smart-I finite element enhanced FEM (SFEE-FEM) is able to conduct the accurate computation with a small number of elements, and thus greatly reduces the time cost. The smart-I finite element proposed by this work breaks through the limitation of traditional element shape with regular boundary (e.g., straight line), and may pave a new way to implement the FEM calculation on voxel-based geometries efficiently.