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WIREs Comput Mol Sci
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Encoding the atomic structure for machine learning in materials science

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Abstract In recent years, we have witnessed a widespread application of machine learning techniques in the field of materials science, owing to the increased availability of research data and sophisticated algorithms. At the core of this technology lies the ability to encode material structures into descriptors that are understandable for a computer. Although significant advances have been made in this area, there is a continued need to explore efficient structure‐encoding strategies so as to maximize the predictive power of the machine learning models. Here we present a revision of the exciting progress in four representative structural features that are capable of describing the structures of diverse materials: structure graph, Coulomb matrix, topological descriptor, and diffraction fingerprint. Particular attention is given to the studies of crystalline solids, which appear more challenging to be encoded than molecules. By summarizing previous works and presenting critical appraisals of these descriptors, this review could offer some guideline for the selection of structural features and stimulate inspiration for the design of powerful descriptors suited towards different tasks. This article is categorized under: Structure and Mechanism > Computational Materials Science Data Science > Artificial Intelligence/Machine Learning
(a) The structure graph of 2‐methylpentane and the corresponding adjacency matrix, additive adjacency matrix and distance matrix (reprinted with permission from Reference 64). (b) Schematic illustration of the construction of PLMF descriptors (reprinted with permission from Reference 60). (c) The subgraphs of spinel Co3O4 (reprinted with permission from Reference 75)
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(a) XRD patterns of typical solid‐state Li ion conductors and materials after unsupervised clustering (reprinted with permission from Reference 146). (b) Construction of descriptor from real‐space and reciprocal‐space representations (reprinted with permission from Reference 153)
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The construction of 2D diffraction fingerprints and examples of diffraction patterns for materials belonging to the selected crystal structures (reprinted with permission from Reference 141)
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(a) Cyclohexane and its persistent barcodes with all elements and the carbon element selected, respectively (reprinted with permission from Reference 137). (b) The construction of element‐specific topological descriptor for BaTiO3 (reprinted with permission from Reference 138)
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(a) The filtration of the distance function to a point cloud and the construction of persistent barcodes (reprinted with permission from Reference 124). (b) The flowchart for the construction of topological fingerprint of a Li cluster (reprinted with permission from Reference 135). (c) The persistent barcode of pore structure in the zeolite PCOD8331112 (reprinted with permission from Reference 136)
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(a) Φ(Ri, Rj) in the sine matrix representation for a 2D crystal lattice, where periodicity is shown (reprinted with permission from Reference 94). (b) Comparison of Coulomb, Ewald sum, and sine matrices in the representation of a periodic diamond structure (reprinted with permission from Reference 106)
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(a) Representation of a molecule via Coulomb matrix (reprinted with permission from Reference 65). (b) Permutationally invariant representations based on Coulomb matrix: its eigenspectrum, the sorted version and a set of randomly sorted Coulomb matrices (reprinted with permission from Reference 98). (c) Structure of ethanol and its representation in Coulomb matrix, the bags of different bond types, and the BoB vector (reprinted with permission from Reference 100)
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(a) Construction of structure graph that satisfies the periodic conditions in the CGCNN model (reprinted with permission from Reference 90). (b) MEGNet models based on graph convolutions of atomic, bond and global state attributes (reprinted with permission from Reference 96)
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(Left) Construction of element feature matrices for 2D materials. (Right) Selection of element feature matrices for target properties (reprinted with permission from Reference 79)
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Structure and Mechanism > Computational Materials Science

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