Towards Generalized Noise-level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

Moeck, Peter

doi:10.20944/preprints201804.0083.v1

Cited by 3 publications

(1 citation statement)

References 96 publications

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“…As an important note, our classification task is different from the standard image classification task due to the hierarchical nature of crystal symmetries. Crystallography is inherently hierarchical and continuous for any real material system 44,45 . Under enough noise, for example, a slight tetragonal distortion to a cubic structure will be indistinguishable from a standard cubic structure.…”

Section: Classification Experiments With Varying Numbers Of Sgsmentioning

confidence: 99%

Identification of crystal symmetry from noisy diffraction patterns by a shape analysis and deep learning

et al. 2020

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The robust and automated determination of crystal symmetry is of utmost importance in material characterization and analysis. Recent studies have shown that deep learning (DL) methods can effectively reveal the correlations between X-ray or electron-beam diffraction patterns and crystal symmetry. Despite their promise, most of these studies have been limited to identifying relatively few classes into which a target material may be grouped. On the other hand, the DL-based identification of crystal symmetry suffers from a drastic drop in accuracy for problems involving classification into tens or hundreds of symmetry classes (e.g., up to 230 space groups), severely limiting its practical usage. Here, we demonstrate that a combined approach of shaping diffraction patterns and implementing them in a multistream DenseNet (MSDN) substantially improves the accuracy of classification. Even with an imbalanced dataset of 108,658 individual crystals sampled from 72 space groups, our model achieves 80.12 ± 0.09% space group classification accuracy, outperforming conventional benchmark models by 17–27 percentage points (%p). The enhancement can be largely attributed to the pattern shaping strategy, through which the subtle changes in patterns between symmetrically close crystal systems (e.g., monoclinic vs. orthorhombic or trigonal vs. hexagonal) are well differentiated. We additionally find that the MSDN architecture is advantageous for capturing patterns in a richer but less redundant manner relative to conventional convolutional neural networks. The proposed protocols in regard to both input descriptor processing and DL architecture enable accurate space group classification and thus improve the practical usage of the DL approach in crystal symmetry identification.

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Section: Classification Experiments With Varying Numbers Of Sgsmentioning

confidence: 99%

Identification of crystal symmetry from noisy diffraction patterns by a shape analysis and deep learning

et al. 2020

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Mapping mesoscopic phase evolution during E-beam induced transformations via deep learning of atomically resolved images

et al. 2018

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Understanding transformations under electron beam irradiation requires mapping the structural phases and their evolution in real time. To date, this has mostly been a manual endeavor comprising of difficult frame-by-frame analysis that is simultaneously tedious and prone to error. Here, we turn towards the use of deep convolutional neural networks (DCNN) to automatically determine the Bravais lattice symmetry present in atomically-resolved images. A DCNN is trained to identify the Bravais lattice class given a 2D fast Fourier transform of the input image. Monte-Carlo dropout is used for determining the prediction probability, and results are shown for both simulated and real atomically-resolved images from scanning tunneling microscopy and scanning transmission electron microscopy. A reduced representation of the final layer output allows to visualize the separation of classes in the DCNN and agrees with physical intuition. We then apply the trained network to electron beam-induced transformations in WS2, which allows tracking and determination of growth rate of voids. These results are novel in two ways: (1) It shows that DCNNs can be trained to recognize diffraction patterns, which is markedly different from the typical 'real image' cases, and (2) it provides a method with in-built uncertainty quantification, allowing the real-time analysis of phases present in atomically resolved images.

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Accurate lattice parameters from 2D-periodic images for subsequent Bravais lattice type assignments

Moeck

DeStefano

2018

Adv Struct Chem Imag

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Three different algorithms, as implemented in three different computer programs, were put to the task of extracting direct space lattice parameters from four sets of synthetic images that were per design more or less periodic in two dimensions (2D). One of the test images in each set was per design free of noise and, therefore, genuinely 2D periodic so that it adhered perfectly to the constraints of a Bravais lattice type, Laue class, and plane symmetry group. Gaussian noise with a mean of zero and standard deviations of 10 and 50% of the maximal pixel intensity was added to the individual pixels of the noise-free images individually to create two more images and thereby complete the sets. The added noise broke the strict translation and site/point symmetries of the noise-free images of the four test sets so that all symmetries that existed per design turned into pseudo-symmetries of the second kind. Moreover, motif and translation-based pseudo-symmetries of the first kind, a.k.a. genuine pseudo-symmetries, and a metric specialization were present per design in the majority of the noise-free test images already. With the extraction of the lattice parameters from the images of the synthetic test sets, we assessed the robustness of the algorithms’ performances in the presence of both Gaussian noise and pre-designed pseudo-symmetries. By applying three different computer programs to the same image sets, we also tested the reliability of the programs with respect to subsequent geometric inferences such as Bravais lattice type assignments. Partly due to per design existing pseudo-symmetries of the first kind, the lattice parameters that the utilized computer programs extracted in their default settings disagreed for some of the test images even in the absence of noise, i.e., in the absence of pseudo-symmetries of the second kind, for any reasonable error estimates. For the noisy images, the disagreement of the lattice parameter extraction results from the algorithms was typically more pronounced. Non-default settings and re-interpretations/re-calculations on the basis of program outputs allowed for a reduction (but not a complete elimination) of the differences in the geometric feature extraction results of the three tested algorithms. Our lattice parameter extraction results are, thus, an illustration of Kenichi Kanatani’s dictum that no extraction algorithm for geometric features from images leads to definitive results because they are all aiming at an intrinsically impossible task in all real-world applications (Kanatani in Syst Comput Jpn 35:1–9, 2004). Since 2D-Bravais lattice type assignments are the natural end result of lattice parameter extractions from more or less 2D-periodic images, there is also a section in this paper that describes the intertwined metric relations/holohedral plane and point group symmetry hierarchy of the five translation symmetry types of the Euclidean plane. Because there is no definitive lattice parameter extraction algorithm, the outputs of computer programs that implemented such al...

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Towards Generalized Noise-level Dependent Crystallographic Symmetry Classifications of More or Less Periodic Crystal Patterns

Cited by 3 publications

References 96 publications

Identification of crystal symmetry from noisy diffraction patterns by a shape analysis and deep learning

Identification of crystal symmetry from noisy diffraction patterns by a shape analysis and deep learning

Mapping mesoscopic phase evolution during E-beam induced transformations via deep learning of atomically resolved images

Accurate lattice parameters from 2D-periodic images for subsequent Bravais lattice type assignments

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