Inverting the Kohn–Sham equations with physics-informed machine learning
Electronic structure theory calculations offer an understanding of matter at the quantum level, complementing experimental studies in materials science and chemistry. One of the most widely used methods, density functional theory, maps a set of real interacting electrons to a set of fictitious non-i...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/ad3159 |
| _version_ | 1797257392198516736 |
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| author | Vincent Martinetto Karan Shah Attila Cangi Aurora Pribram-Jones |
| author_facet | Vincent Martinetto Karan Shah Attila Cangi Aurora Pribram-Jones |
| author_sort | Vincent Martinetto |
| collection | DOAJ |
| description | Electronic structure theory calculations offer an understanding of matter at the quantum level, complementing experimental studies in materials science and chemistry. One of the most widely used methods, density functional theory, maps a set of real interacting electrons to a set of fictitious non-interacting electrons that share the same probability density. Ensuring that the density remains the same depends on the exchange-correlation (XC) energy and, by a derivative, the XC potential. Inversions provide a method to obtain exact XC potentials from target electronic densities, in hopes of gaining insights into accuracy-boosting approximations. Neural networks provide a new avenue to perform inversions by learning the mapping from density to potential. In this work, we learn this mapping using physics-informed machine learning methods, namely physics informed neural networks and Fourier neural operators. We demonstrate the capabilities of these two methods on a dataset of one-dimensional atomic and molecular models. The capabilities of each approach are discussed in conjunction with this proof-of-concept presentation. The primary finding of our investigation is that the combination of both approaches has the greatest potential for inverting the Kohn–Sham equations at scale. |
| first_indexed | 2024-04-24T22:36:54Z |
| format | Article |
| id | doaj.art-75909b6cef20449880b2f3982d4b148e |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-04-24T22:36:54Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-75909b6cef20449880b2f3982d4b148e2024-03-19T08:30:49ZengIOP PublishingMachine Learning: Science and Technology2632-21532024-01-015101505010.1088/2632-2153/ad3159Inverting the Kohn–Sham equations with physics-informed machine learningVincent Martinetto0https://orcid.org/0000-0001-6026-7397Karan Shah1https://orcid.org/0000-0002-5480-2880Attila Cangi2https://orcid.org/0000-0001-9162-262XAurora Pribram-Jones3https://orcid.org/0000-0003-0244-1814Department of Chemistry and Biochemistry, University of California Merced , 5200 North Lake Rd., Merced, CA 95343, United States of AmericaCenter for Advanced Systems Understanding , 02826 Görlitz, Germany; Helmholtz-Zentrum Dresden-Rossendorf , 01328 Dresden, GermanyCenter for Advanced Systems Understanding , 02826 Görlitz, Germany; Helmholtz-Zentrum Dresden-Rossendorf , 01328 Dresden, GermanyDepartment of Chemistry and Biochemistry, University of California Merced , 5200 North Lake Rd., Merced, CA 95343, United States of AmericaElectronic structure theory calculations offer an understanding of matter at the quantum level, complementing experimental studies in materials science and chemistry. One of the most widely used methods, density functional theory, maps a set of real interacting electrons to a set of fictitious non-interacting electrons that share the same probability density. Ensuring that the density remains the same depends on the exchange-correlation (XC) energy and, by a derivative, the XC potential. Inversions provide a method to obtain exact XC potentials from target electronic densities, in hopes of gaining insights into accuracy-boosting approximations. Neural networks provide a new avenue to perform inversions by learning the mapping from density to potential. In this work, we learn this mapping using physics-informed machine learning methods, namely physics informed neural networks and Fourier neural operators. We demonstrate the capabilities of these two methods on a dataset of one-dimensional atomic and molecular models. The capabilities of each approach are discussed in conjunction with this proof-of-concept presentation. The primary finding of our investigation is that the combination of both approaches has the greatest potential for inverting the Kohn–Sham equations at scale.https://doi.org/10.1088/2632-2153/ad3159physics-informed neural networksdensity-to-potential inversionsdensity functional theoryneural operators |
| spellingShingle | Vincent Martinetto Karan Shah Attila Cangi Aurora Pribram-Jones Inverting the Kohn–Sham equations with physics-informed machine learning Machine Learning: Science and Technology physics-informed neural networks density-to-potential inversions density functional theory neural operators |
| title | Inverting the Kohn–Sham equations with physics-informed machine learning |
| title_full | Inverting the Kohn–Sham equations with physics-informed machine learning |
| title_fullStr | Inverting the Kohn–Sham equations with physics-informed machine learning |
| title_full_unstemmed | Inverting the Kohn–Sham equations with physics-informed machine learning |
| title_short | Inverting the Kohn–Sham equations with physics-informed machine learning |
| title_sort | inverting the kohn sham equations with physics informed machine learning |
| topic | physics-informed neural networks density-to-potential inversions density functional theory neural operators |
| url | https://doi.org/10.1088/2632-2153/ad3159 |
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