Predicting Young’s Moduli of Nanopillars by Interpretable Machine Learning

Abstract

Understanding the relationship between the atomic structure and mechanical properties of materials is a fundamental problem in materials science. The field of machine learning has seen rapid progress in recent years, leading to its application in a wide variety of fields, including materials science. Neural networks have been successfully employed to predict mechanical properties of materials from their atomic structure. However, a weakness of neural networks is that they are "black box models", as their decision process is not easily comprehensible by humans. Therefore, methods for interpreting neural networks are actively researched. In the context of materials science, interpretable neural networks have the potential to not only accurately model the relationship between the atomic structure and mechanical properties of materials, but also to deepen human understanding of the relationship.

This thesis studies the relationship between the atomic structure and Young’s moduli of polycrystalline nanopillars by interpretable machine learning. The goal of this thesis is to train a convolutional neural network (CNN) to predict the Young’s moduli of nanopillars from their atomic structures, and to interpret the neural network.

A dataset is created in order to train the CNN. A set of polycrystalline tantalum nanopillars are numerically generated, and their Young's moduli are measured by deforming them in molecular dynamics simulations. As an input to the CNN, three different fields are extracted from the atomic structures of the nanopillars, which represent grain boundary atom densities, lattice orientations, and raw atom positions. CNNs are trained to predict the Young's moduli from each of these representations of the initial state. It is found that the prediction accuracy is poor with the grain boundary atom densities, indicating that the grain boundaries contain minimal information about the Young's modulus. In contrast, a very high prediction accuracy is achieved using lattice orientations and even slightly higher with raw atom positions.

Gradient-weighted class activation mapping (Grad-CAM) is used to interpret the CNNs. This method generates fields that represent how different areas of a CNN's inputs influence the produced outputs. Grad-CAM fields are extracted from different convolutional layers of the CNNs for the input pillars. Local Young's modulus fields are calculated based on local lattice orientations, and the correlation between the Grad-CAM fields and local Young's modulus fields is studied. It is found that there is a strong positive correlation between the two fields.

In conclusion, the first goal of training a neural network to predict the Young's moduli of nanopillars from their atomic structures was successfully met. The second goal of interpreting the neural network was achieved to some degree, but further research could be conducted to make the interpretation more comprehensive.