期刊
PHYSICAL REVIEW B
卷 95, 期 21, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.95.214302
关键词
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资金
- Engineering and Physical Sciences Research Council (EPSRC) through the Centre for Doctoral Training Cross Disciplinary Approaches to Non-Equilibrium Systems (CANES) [EP/L015854/1]
- Office of Naval Research Global (ONRG) [N62909-15-1-N079]
- EPSRC HEmS [EP/L014742/1]
- European Union's Horizon research and innovation program [676580]
- Office of Science of the US Department of Energy [DE-AC02-06CH11357]
- Engineering and Physical Sciences Research Council [EP/C523938/1, 1506279] Funding Source: researchfish
- EPSRC [EP/C523938/1] Funding Source: UKRI
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 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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