A CNN-based surrogate model of isogeometric analysis in nonlocal flexoelectric problems

We proposed a convolutional neural network (CNN)-based surrogate model to predict the nonlocal response for flexoelectric structures with complex topologies. The input, i.e. the binary images, for the CNN is obtained by converting geometries into pixels, while the output comes from simulations of an isogeometric (IGA) flexoelectric model, which in turn exploits the higher-order continuity of the underlying non-uniform rational B-splines (NURBS) basis functions to fast computing of flexoelectric parameters, e.g., electric gradient, mechanical displacement, strain, and strain gradient. To generate the dataset of porous flexoelectric cantilevers, we developed a NURBS trimming technique based on the IGA model. As for CNN construction, the key factors were optimized based on the IGA dataset, including activation functions, dropout layers, and optimizers. Then the cross-validation was conducted to test the CNN's generalization ability. Last but not least, the potential of the CNN performance has been explored under different model output sizes and the corresponding possible optimal model layout is proposed. The results can be instructive for studies on deep learning of other nonlocal mech-physical simulations.