An ANN-assisted efficient enriched finite element method via the selective enrichment of moment fitting

Enrichment techniques that employ nonconforming mesh are effective in modeling structures with discontinuities because numerical issues regarding mesh quality are avoided. However, the accurate integration of the bilinear and linear forms on the discretized domain, which is required in the standard Galerkin-based finite element method, is computationally expensive due to the complexity of the enriched basis function. In this paper, we present a fast and accurate alternative method of numerical integration using nonlinear regression enabled by a multi-perceptron feedforward neural network. The relationship between an implicitly represented geometry and the quadrature rule derived from the moment fitting method is predicted by the neural network; the neural network-based regression model circumvents complex computation and significantly reduces the overall online time by avoiding expensive function evaluations. Through the selected numerical examples, we demonstrate the efficiency and accuracy of the current method, as well as the flexibility of the trained network to be used in different contexts.