[Paper Review] Structural Characterization of Grain Boundaries and Machine Learning of Grain Boundary Energy and Mobility

Conrad W. Rosenbrock, Jonathan L. Priedeman+2 more|arXiv (Cornell University)|Aug 15, 2018

Metallurgy and Material Forming13 references4 citations

TL;DR

This paper introduces a machine learning framework for predicting grain boundary (GB) energy, mobility, and shear coupling using two novel atomic structure descriptors: the Averaged SOAP Representation (ASR) and the Local Environment Representation (LER), derived from the Smooth Overlap of Atomic Positions (SOAP) formalism. The LER, which encodes fractions of unique local atomic environments, achieved 85.5% accuracy in classifying GB mobility and 64% in shear coupling prediction, demonstrating that local atomic structure alone can predict key GB properties with high fidelity.

ABSTRACT

Recent advances in the numerical representation of materials opened the way for successful machine learning of grain boundary (GB) energies and the classification of GB mobility and shear coupling. Two representations were needed for these machine learning applications: 1) the ASR representation, based on averaged local environment descriptors; and 2) the LER descriptor, based on fractions of globally unique local environments within the entire GB system. We present a detailed tutorial on how to construct these two representations to learn energy, mobility and shear coupling. Additionally, we catalog some of the null results encountered along the way.

Motivation & Objective

• To develop a physically invariant, differentiable, and smooth representation of grain boundary atomic structures for machine learning applications.
• To enable accurate prediction of grain boundary energy, mobility, and shear coupling using local atomic environment descriptors.
• To address the challenge of high-dimensional configurational space in grain boundaries by identifying universal structural building blocks.
• To evaluate the performance of different machine learning models using ASR and LER descriptors on real GB data.
• To identify limitations in data sparsity, particularly for rare mobility classes like 'constant' mobility.

Proposed method

• Construct the SOAP descriptor for each local atomic environment (LAE) using Gaussian-weighted neighbor density and spherical harmonic expansion.
• Apply rotational and permutational invariance via Wigner D-matrices and integration over SO(3), yielding a rotationally invariant kernel.
• Form the Averaged SOAP Representation (ASR) by averaging SOAP descriptors across all atoms in the GB system.
• Construct the Local Environment Representation (LER) by identifying globally unique LAEs in the GB and computing their fractional contributions.
• Use support vector regression (SVR) with the ASR for grain boundary energy prediction.
• Apply XGBoost and linear SVM with ℓ₁ regularization to classify GB mobility and shear coupling using the LER descriptor.

Experimental results

Research questions

• RQ1 Can a smooth, differentiable, and physically invariant descriptor accurately represent the atomic structure of grain boundaries for machine learning?
• RQ2 To what extent can grain boundary energy be predicted from local atomic environments using the ASR descriptor?
• RQ3 Can GB mobility and shear coupling be classified with high accuracy using only local atomic environment information via the LER descriptor?
• RQ4 How do hyperparameters such as radial basis size and angular cutoff affect the performance of the LER descriptor?
• RQ5 Why does the model fail to learn the 'constant' mobility class, and what does this imply about data sparsity and model generalization?

Key findings

• The LER descriptor achieved 85.5% accuracy in classifying grain boundary mobility on the validation set when the under-represented 'constant' class was excluded.
• Using borderline SMOTE for class balancing and XGBoost, the model achieved over 80% accuracy in mobility classification, significantly outperforming baseline models.
• Shear coupling prediction reached 64% accuracy using a linear SVM with ℓ₁ regularization, though tree-based models performed poorly, suggesting limitations of local environment data for this property.
• The ASR-based energy prediction model achieved 83.0% accuracy on the test set, slightly better than random, but provided no physical insight due to lack of interpretability.
• The LER descriptor is sensitive to parameter choices such as radial basis size and angular cutoff, which influence the number of unique LAEs and thus model performance.
• The study identifies that the 'constant' mobility class is unlearnable with current data size (only 5 GBs), indicating a need for larger datasets to capture rare structural motifs.