Accurate interatomic force fields via machine learning with covariant kernels

By Aldo Glielmo, Peter Sollich, A. De Vita. 2016

175 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Materials Chemistry

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Yuri Mishin
2. Evgeny V. Podryabinkin
3. G. P. P. Pun
4. Rohit Batra
5. Alexander V. Shapeev
6. Rampi Ramprasad
7. A. Mannodi‐Kanakkithodi
8. Ghanshyam Pilania

In Computational Theory and Mathematics

1. Yuri Mishin
2. Rohit Batra
3. Alexander V. Shapeev
4. Rampi Ramprasad
5. Evgeny V. Podryabinkin
6. G. P. P. Pun
7. Michael S. Steinbach
8. Vipin Kumar

In Materials Chemistry

1. Yuri Mishin
2. Evgeny V. Podryabinkin
3. Rohit Batra
4. Rampi Ramprasad
5. Alexander V. Shapeev
6. G. P. P. Pun
7. Chiho Kim
8. A. Mannodi‐Kanakkithodi

Citations in the corpus

• Active learning of linearly parametrized interatomic potentials (2016, methodology): “Three closely related works, [28, 29, 30], use Gaussian process regression to predict the forces on atoms directly, without predicting the energy and taking its gradient.”
• Physically informed artificial neural networks for atomistic modeling of materials (2018, methodology): “The general idea is to forego the physical insights and reproduce the PES by interpolating between DFT data points using high-dimensional nonlinear regression methods such as the Gaussian process regression [19, 25–27], interpolating moving least squares [28], kernel ridge regression [12, 20, 21], c”
• Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “More recently, Glielmo et al. [108] propose a vectorial GPR that encodes physical knowledge in the matrix-valued kernel function.”
• Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, background): “More recently, Glielmo et al. [94] propose a vectorial GPR that encodes physical knowledge in the matrix-valued kernel function.”
• Machine Learning and Materials Informatics: Recent Applications and Prospects (2017, background): “These truly vectorial or tensorial target property cases will thus have to be handled with care, as has been done recently using vector learning and covariant kernels [91].”