Machine learning models of plastic flow based on representation theory

TL;DR

This paper employs machine learning, specifically neural networks, to model stress and plastic flow in polycrystalline materials, integrating classical modeling principles to enhance accuracy and interpretability.

Contribution

It introduces a ML framework that incorporates classical symmetries for modeling plastic flow, enabling rapid and physically consistent predictions.

Findings

Neural networks effectively model stress and plastic flow responses.

Incorporating classical symmetries improves model accuracy and interpretability.

Framework facilitates real-time predictions and guides data collection.

Abstract

We use machine learning (ML) to infer stress and plastic flow rules using data from repre- sentative polycrystalline simulations. In particular, we use so-called deep (multilayer) neural networks (NN) to represent the two response functions. The ML process does not choose ap- propriate inputs or outputs, rather it is trained on selected inputs and output. Likewise, its discrimination of features is crucially connected to the chosen input-output map. Hence, we draw upon classical constitutive modeling to select inputs and enforce well-accepted symmetries and other properties. With these developments, we enable rapid model building in real-time with experiments, and guide data collection and feature discovery.