Predicting mechanical fields near cracks using a progressive transformer diffusion model and exploration of generalization capacity

We report a deep learning method to predict high-resolution stress fields from material microstructures, using a novel class of progressive attention-based transformer diffusion models. We train the model with a small dataset of pairs of input microstructures and resulting atomic-level Von Mises stress fields obtained from molecular dynamics (MD) simulations, and show excellent capacity to accurately predict results. We conduct a series of computational experiments to explore generalizability of the model and show that while the model was trained on a small dataset that featured samples of multiple cracks, the model can accurately predict distinct fracture scenarios such as single cracks, or crack-like defects with very different shapes. A comparison with MD simulations provides excellent comparison to the ground truth results in all cases. The results indicate that exciting opportunities that lie ahead in using progressive transformer diffusion models in the physical sciences, to produce high-fidelity and high-resolution field images.

Automated summary

We propose a deep learning method for predicting high-resolution stress fields from material microstructures using a novel class of progressive attention-based transformer diffusion models. The model is trained on a small dataset of input microstructures and corresponding atomic-level Von Mises stress fields obtained from molecular dynamics simulations, and demonstrates excellent accuracy in predicting results. Computational experiments show that the model can accurately predict distinct fracture scenarios, even when trained on a small dataset featuring samples of multiple cracks. Comparison with molecular dynamics simulations confirms the model's high fidelity in all cases, highlighting the exciting potential of progressive transformer diffusion models in the physical sciences for producing high-resolution field images.