  This work presents a machine learning approach to predict peak-stress
clusters in heterogeneous polycrystalline materials. Prior work on using
machine learning in the context of mechanics has largely focused on predicting
the effective response and overall structure of stress fields. However, their
ability to predict peak stresses -- which are of critical importance to failure
-- is unexplored, because the peak-stress clusters occupy a small spatial
volume relative to the entire domain, and hence requires computationally
expensive training. This work develops a deep-learning based Convolutional
Encoder-Decoder method that focuses on predicting peak-stress clusters,
specifically on the size and other characteristics of the clusters in the
framework of heterogeneous linear elasticity. This method is based on
convolutional filters that model local spatial relations between
microstructures and stress fields using spatially weighted averaging
operations. The model is first trained against linear elastic calculations of
stress under applied macroscopic strain in synthetically-generated
microstructures, which serves as the ground truth. The trained model is then
applied to predict the stress field given a (synthetically-generated)
microstructure and then to detect peak-stress clusters within the predicted
stress field. The accuracy of the peak-stress predictions is analyzed using the
cosine similarity metric and by comparing the geometric characteristics of the
peak-stress clusters against the ground-truth calculations. It is observed that
the model is able to learn and predict the geometric details of the peak-stress
clusters and, in particular, performed better for higher (normalized) values of
the peak stress as compared to lower values of the peak stress. These
comparisons showed that the proposed method is well-suited to predict the
characteristics of peak-stress clusters.

Analysis of PDEs;Materials Science