Development of Surrogate Model to Predict Errors in FEM solutions using Deep Convolutional Neural Networks

View Video Presentation: https://doi.org/10.2514/6.2022-0972.vid This research is a proof-of-concept to develop a surrogate model, using deep learning (DL) to predict solution error for a given model with a generated mesh. For this research, we have taken von-Mises stress and predicting error in von-Mises stress contour due to poor meshing using a deep learning network called Convolution Neural Network (CNN). In advanced Finite Element (FE) packages error indicators are used to extract this information and also to perform adaptive mesh refinement to increase the solution accuracy. Adaptive re-meshing is an iterative process to reduce down the error but it is computationally expensive and thus we propose an approach to replace it using data-driven techniques. The developed approach provides an approximate prediction of solution error along with their maximum and minimum location. This information can be used as a mesh modeling recommendation for improving overall mesh quality. The proposed method can be seen as an image-to-image regression problem where the input datasets are the images of von-Mises stress contours and the output are the error indicator images. Both of these image datasets are generated using Abaqus Python scripting capabilities. To train this model with good generalization performance, the entire dataset comprises of four small unique datasets and it is divided into three small training subsets. Each unique dataset is a collection of 1000 stress images and their corresponding error images for a plate with a hole model where each of the small datasets varies in hole sizes. The entire research is implemented in a two-phase approach, Phase I involves the design and development of a CNN to perform training on stress images with their corresponding von-Mises stress values volume-averaged over the entire domain. Phase II involves developing a surrogate model to perform image-to-image regression which comprises of two auto encoder networks, one Encoder-Decoder assembly, and one multi-output regression neural network.