Prediction of atomic stress fields using cycle-consistent adversarial neural networks based on unpaired and unmatched sparse datasets.

Deep learning holds great promise for applications in materials science, including the discovery of physical laws and materials design. However, the availability of proper data remains a challenge - often, data lacks labels, or does not contain direct pairing between input and output property of interest. Here we report an approach based on an adversarial neural network model - composed of four individual deep neural nets - to yield atomistic-level prediction of stress fields directly from an input atomic microstructure, illustrated here for defected graphene sheets under tension. The primary question we address is whether it is possible to predict stress fields without any microstructure-to-stress fields pairings, nor the existence of any input-output pairs whatsoever, in the dataset. Using a cycle-consistent adversarial neural net with either U-Net, ResNet and a hybrid U-Net-ResNet architecture, applied to a system of graphene lattices with defects we devise an algorithmic framework that enables us to successfully train and validate a model that reliably predicts atomistic-level field data of unknown microstructures, generalizing to reproduce well-known nano- and micromechanical features such as stress concentrations, size effects, and crack shielding. In a series of validation analyses, we show that the model closely reproduces reactive molecular dynamics simulations but at significant computational efficiency, and without knowledge of any physical laws that govern this complex fracture problem. The model opens an avenue for upscaling where the mechanistic insights, and predictions from the model, can be used to construct analyses of very large systems, based off relatively small and sparse datasets. Since the model is trained to achieve cycle consistency, a trained model features both forward (microstructure to stress) and inverse (stress to microstructure) generators; offering potential applications in materials design to achieve a certain stress field. Another application is the prediction of stress fields based off experimentally acquired structural data, where the knowledge of solely positions of atoms is sufficient to predict physical quantities for augmentation or analysis processes.