Efficient integration of deep neural networks in sequential multiscale simulations

Abstract

AbstractMultiscale computations involving finite elements are often unfeasible due to their substantial computational costs arising from numerous microstructure evaluations. This necessitates the utilization of suitable surrogate models, which can be rapidly evaluated. In this work, we apply a purely data‐based deep neural network as a surrogate model for the microstructure evaluation. More precisely, the surrogate model predicts the homogenized stresses, which are typically obtained by the solution of (initial) boundary‐value problems of a microstructure and subsequent homogenization. Furthermore, the required consistent tangent matrix is computed by leveraging reverse mode automatic differentiation. To improve data efficiency and ensure high prediction quality, the well‐known Sobolev training is chosen for creating the surrogate model. This surrogate model is seamlessly integrated into a Fortran‐based finite element code using an open‐source library. As a result, this integration, combined with just‐in‐time compilation, leads to a speed‐up of more than 6000× , as demonstrated in the example of a plate with a hole examined in this work. Furthermore, the surrogate model proves to be applicable even in load‐step size controlled simulations, where it overcomes certain load‐step size limitations associated with the microstructure computations.