Double U‐net : improved multiscale modeling via fully convolutional neural networks

Abstract

In multiscale modeling, the response of the macroscopic material is computed by considering the behavior of the microscale at each material point. To keep the computational overhead low when simulating such high performance materials, an efficient, but also very accurate prediction of the microscopic behavior is of utmost importance. Artificial neural networks are well known for their fast and efficient evaluation. We deploy fully convolutional neural networks, with one advantage being that, compared to neural networks directly predicting the homogenized response, any quantity of interest can be recovered from the solution, for example, peak stresses relevant for material failure. We propose a novel model layout, which outperforms state‐of‐the‐art models with fewer model parameters. This is achieved through a staggered optimization scheme ensuring an accurate low‐frequency prediction. The prediction is further improved by superimposing an efficient to evaluate U‐net, which captures the remaining high‐level features.