Source-linked AI summary
Insightful classification of crystal structures using deep learning
A. Ziletti, D. Kumar, M. Scheffler, L. M. Ghiringhelli
TL;DR
Existing crystal-symmetry identification requires user-specified thresholds and can fail on defective structures, limiting reliable analysis of noisy three-dimensional data. This paper represents structures with two-dimensional diffraction fingerprints and classifies them using a convolutional neural network. The procedure requires no user-specified threshold and achieves perfect classification even for highly defective structures.
Problem
Current symmetry-identification methods require user-specified thresholds and fail on defective structures, while reliable symmetry recognition is needed for materials characterization and analysis.
Method
The approach represents three-dimensional crystal structures with two-dimensional diffraction fingerprints and uses a convolutional neural network to predict crystal classes.
Results
The procedure requires no user-specified threshold and achieves perfect classification even in the presence of highly defective structures.
Takeaways & Limitations
The method supports automatic crystal classification of potentially noisy and incomplete three-dimensional structural data according to crystal symmetry.
Takeaways & Limitations
The diffraction fingerprint is not unique across space groups and cannot represent non-centrosymmetric structures by construction.
Abstract
from arXiv · showhide
Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and analytics. Current methods require a user-specified threshold, and are unable to detect average symmetries for defective structures. Here, we propose a machine-learning-based approach to automatically classify structures by crystal symmetry. First, we represent crystals by calculating a diffraction image, then construct a deep-learning neural-network model for classification. Our approach is able to correctly classify a dataset comprising more than 100 000 simulated crystal structures, including heavily defective ones. The internal operations of the neural network are unraveled through attentive response maps, demonstrating that it uses the same landmarks a materials scientist would use, although never explicitly instructed to do so. Our study paves the way for crystal-structure recognition of - possibly noisy and incomplete - three-dimensional structural data in big-data materials science.
Introduction
Crystal symmetry is essential for understanding and computing materials properties, but existing symmetry-identification procedures depend on thresholds and struggle with defects. The proposed workflow uses diffraction fingerprints and a convolutional neural network to classify structures automatically while inspecting the model’s physical basis.
- Crystal structure directly affects materials properties, as illustrated by nearly fortyfold higher carbon solubility in fcc γ-Fe than bcc α-Fe.
- Existing symmetry packages determine space groups by comparing allowed symmetry operations with possible space groups, but practical structures often deviate from ideal positions.
- High-throughput materials science lacks a universal threshold for millions of calculations, while defects can defeat symmetry-based approaches regardless of tolerance settings.
- Atom-probe tomography supplies near-atomic-resolution three-dimensional positions but can miss at least 20% of atoms and has substantial positional uncertainty.
- The workflow represents structures as two-dimensional diffraction fingerprints, trains a convolutional neural network on a subset, visualizes its internal operations, and deploys the resulting classifier.
Results
The study represents crystals with two-dimensional diffraction fingerprints and classifies them using a deep-learning ConvNet, avoiding hand-crafted peak-detection rules. The approach achieves perfect pristine-dataset accuracy, remains robust to severe defects, and learns interpretable diffraction-based class features.
- How to represent a material: Two-dimensional diffraction fingerprints compactly encode periodicity and crystal symmetry while remaining invariant to system size.They emphasize atomic positions and symmetry more than atomic species, allowing extended and finite systems to be treated on equal footing.
- How to represent a material: The diffraction fingerprint is not unique across space groups and cannot represent non-centrosymmetric structures by construction.Among the eight considered prototypes, rhombohedral and hexagonal structures share the same fingerprint and are therefore merged into one class.
- The classification model: A ConvNet replaces ad-hoc diffraction-peak rules by learning hierarchical representations from labeled fingerprint images and minimizing classification error.The descriptor is generated from simulated scattering, with rotated diffraction patterns superimposed before classification.
- The model performance: 100% accuracy was obtained on both training and test sets for the pristine dataset, with training taking 80 minutes and prediction about 70 ms per fingerprint.The dataset was assembled from eight centrosymmetric space-group classes represented by more than 50 configurations each, with rhombohedral and hexagonal structures merged.
- The model performance: The model correctly classified randomly displaced structures up to σ = 0.06 Å and achieved 100% accuracy up to 40% vacancies, exceeding 97% at 60% vacancies.Spglib accuracy depended strongly on its threshold and fell to approximately 0% at only 1% vacancies; no defective structures were included during training.
- The model performance: For a bcc-to-sc transition, classification probabilities shifted near 75% removal of central atoms and became certain again for pure sc structures.The percentage of removed central atoms acts as an order parameter, while the network expresses uncertainty for intermediate structures.
Discussion
The paper introduces an interpretable diffraction-fingerprint representation and a convolutional neural network for automatic crystal-class prediction without user-specified thresholds, including highly defective structures.
- The two-dimensional diffraction fingerprint compactly encodes crystal symmetries in reciprocal space and complements real-space representations.Its physical basis supports crystal classification while retaining interpretability.
- A convolutional neural network uses diffraction fingerprints to predict crystal classes automatically.
- The procedure requires no user-specified threshold and achieves perfect classification in the presence of highly defective structures.
- The authors identify defective datasets as a stringent test of analytics-model generalization in materials science.
Methods
The methods generate randomized, finite crystal samples, convert them into diffraction fingerprints, and classify them with a trained convolutional neural network using curated and defect-modified datasets.
- Dataset and preprocessing: Structures are randomly rotated, converted to conventional cells, and processed without symmetry detection during cell construction.The implementation uses customized pymatgen-based procedures and a triclinic-cell convention.
- Dataset and preprocessing: Finite samples are isotropically scaled by average nearest-neighbor bond length to test local structure recognition.
- Diffraction fingerprint: Hydrogen and helium receive augmented atomic-number values because their low electron counts produce weak diffraction-fingerprint contrast.The study targets a transferable computational descriptor rather than direct comparison with experimental diffraction data.
- Diffraction fingerprint: Each diffraction fingerprint is a 64×64 image, with the central direct-beam spot removed to improve high-order-peak contrast.Patterns are calculated using Condor.
- Dataset and preprocessing: The pristine dataset draws from AFLOWLIB centrosymmetric space groups with more than 50 configurations and consistent classifications across symmetry tolerances.
- Neural network training: The convolutional neural network is trained with Adam, batches of 32 images, five epochs, learning rate 10^-3, and cross-entropy loss.The implementation uses TensorFlow and Keras.
Additional information
The additional information identifies the paper and its authors and states that the authors report no competing financial interests.
- The authors declare that they have no competing financial interests.
- The supplementary information accompanies “Insightful classification of crystal structures using deep learning.”
- The listed authors are Angelo Ziletti, Devinder Kumar, Matthias Scheffler, and Luca M. Ghiringhelli.
1 Supplementary Note 1
Supplementary Note 1 compares Spglib with the proposed method for identifying the most similar crystal class in defective structures, using displacement and vacancy defects.
- The comparison includes Spglib thresholds labeled tight, medium, and loose, defined by different symmetry-tolerance parameters.
- Supplementary Table 1 reports percentage accuracy for crystal-class identification after randomly displacing atoms with Gaussian standard deviation σ.
- Supplementary Table 2 reports percentage accuracy after randomly removing η% of atoms to create vacancies.
2 Supplementary Note 2
The study tests whether structures progressively disordered by random atomic displacements are classified as amorphous once their Lindemann parameter reaches the solid–liquid transition range. Across fcc, bcc, and bct139 structures, the classification probabilities show qualitatively comparable disorder-dependent behavior, despite training exclusively on pristine structures.
- Structures with Lindemann parameters from 0 to 0.3 were generated by applying random atomic displacements to pristine fcc, bcc, and bct139 structures.The range spans pristine structures at 0 to amorphous structures at 0.3.
- Classification-probability distributions drop around Lindemann parameters 0.1–0.2, the commonly accepted range for a solid–liquid transition.This trend is shown for fcc, bcc, and bct139 structures.
- The bcc and bct139 classes follow quantitatively different but qualitatively comparable trends, although the model was trained exclusively on pristine structures.Thus, the model distinguishes ordered structures with defects from amorphous structures without labeled disordered training examples.