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Accurate interatomic force fields via machine learning with covariant kernels
Open accessAbstract
We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian process (GP) regression. This is based on matrix-valued kernel functions, on which we impose the requirements that the predicted force rotates with the target configuration and is independent of any rotations applied to the configuration database entries. We show that such covariant GP kernels can be obtained by integration over the elements of the rotation group $\mathit{SO}(d)$ for the relevant dimensionality $d$. Remarkably, in specific cases the integration can be carried out analytically and yields a conservative force field that can be recast into a pair interaction form. Finally, we show that restricting the integration to a summation over the elements of a finite point group relevant to the target system is sufficient to recover an accurate GP. The accuracy of our kernels in predicting quantum-mechanical forces in real materials is investigated by tests on pure and defective Ni, Fe, and Si crystalline systems.
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Gaussian Processes for Machine Learning
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Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
Behler, J., & Parrinello, M. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.146401 · Cited by 5,010
Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons
Bartók, A. P., Payne, M. C., Kondor, R., & Csányi, G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.136403 · Cited by 3,242
On representing chemical environments
Bartók, A. P., Kondor, R., & Csányi, G. (2013) · Physical Review B · doi:10.1103/physrevb.87.184115 · Cited by 2,572
Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
Rupp, M., Tkatchenko, A., Müller, K.-R., & von Lilienfeld, O. A. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.058301 · Cited by 2,312
Free Energy Surface Reconstruction from Umbrella Samples Using Gaussian Process Regression
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Cited by
Recent advances and applications of machine learning in solid-state materials science
Schmidt, J., Marques, M. R. G., Botti, S., & Marques, M. A. L. (2019) · npj Computational Materials · doi:10.1038/s41524-019-0221-0 · Cited by 2,607
Machine learning in materials informatics: recent applications and prospects
Ramprasad, R., Batra, R., Pilania, G., Mannodi-Kanakkithodi, A., & Kim, C. (2017) · npj Computational Materials · doi:10.1038/s41524-017-0056-5 · Cited by 1,945
Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems
Keith, J. A., Vassilev-Galindo, V., Cheng, B., Chmiela, S., Gastegger, M., Müller, K.-R., & Tkatchenko, A. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.1c00107 · Cited by 849
Active learning of linearly parametrized interatomic potentials
Podryabinkin, E. V., & Shapeev, A. V. (2017) · Computational Materials Science · doi:10.1016/j.commatsci.2017.08.031 · Cited by 678
Smith, J. S., Nebgen, B. T., Zubatyuk, R., Lubbers, N., Devereux, C., Barros, K., Tretiak, S., Isayev, O., & Roitberg, A. E. (2019) · Nature Communications · doi:10.1038/s41467-019-10827-4 · Cited by 664
Metadata
- Authors
- Glielmo, A., Sollich, P., & De Vita, A.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2017-06-08
- Volume
- 95
- Issue
- 21
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2566573083
- Cited by
- 220
- References
- 6
- FWCI
- 12.42
- Type
- journal article
- Language
- en
- Open access
- bronze
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