Machine Learning of Dislocation-Induced Stress Fields and Interaction Forces

In discrete dislocation dynamics (DDD) simulations dislocation-induced stress fields and dislocation-dislocation interaction forces are typically evaluated using analytically described multiparameter continuous functions. The universal approximation theory guarantees the approximation of such functions by some machine learning (ML) techniques, which in turn can potentially help to accelerate DDD simulations. However, accurate machine approximation is as crucial as its acceleration. Here, we demonstrate the feasibility of utilizing deep neural networks to predict dislocation-induced stress fields and dislocation-dislocation interaction forces. We also show that the trained network produces estimates that are in very good agreement with analytical solutions. This was only plausible by generating an enriched data repository to avoid bias in the training data. This work opens the door to further development of more optimized ML architectures that could lead to a more computationally efficient, yet accurate, approach to replace the generally inefficient analytical calculations of dislocation-dislocation interaction forces in DDD simulations.