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Tensor-reduced atomic density representations
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Darby, James P., Kovács, Dávid P., Batatia, Ilyes, Caro, Miguel A., Hart, Gus L. W., Ortner, Christoph and Csányi, Gábor (2023) Tensor-reduced atomic density representations. Physical Review Letters, 131 (2). 028001. doi:10.1103/PhysRevLett.131.028001 ISSN 0031-9007.
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WRAP-tensor-reduced-atomic-density-representations-Ortner-2023.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (412Kb) | Preview |
Official URL: http://dx.doi.org/10.1103/PhysRevLett.131.028001
Abstract
Density-based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modeling, and the visualization and analysis of material datasets. The standard mechanism used to incorporate chemical element information is to create separate densities for each element and form tensor products between them. This leads to a steep scaling in the size of the representation as the number of elements increases. Graph neural networks, which do not explicitly use density representations, escape this scaling by mapping the chemical element information into a fixed dimensional space in a learnable way. By exploiting symmetry, we recast this approach as tensor factorization of the standard neighbour-density-based descriptors and, using a new notation, identify connections to existing compression algorithms. In doing so, we form compact tensor-reduced representation of the local atomic environment whose size does not depend on the number of chemical elements, is systematically convergable, and therefore remains applicable to a wide range of data analysis and regression tasks.
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QC Physics |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Tensor fields , Euclidean algorithm, Machine learning , Neural networks (Computer science), Graph theory, Quantum theory -- Mathematical models | ||||||||||||||||||
| Journal or Publication Title: | Physical Review Letters | ||||||||||||||||||
| Publisher: | American Physical Society | ||||||||||||||||||
| ISSN: | 0031-9007 | ||||||||||||||||||
| Official Date: | 13 July 2023 | ||||||||||||||||||
| Dates: |
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| Volume: | 131 | ||||||||||||||||||
| Number: | 2 | ||||||||||||||||||
| Article Number: | 028001 | ||||||||||||||||||
| DOI: | 10.1103/PhysRevLett.131.028001 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||
| Date of first compliant deposit: | 20 September 2023 | ||||||||||||||||||
| Date of first compliant Open Access: | 25 September 2023 | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
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