Regularised Atomic Body-Ordered Permutation-Invariant Polynomials for the Construction of Interatomic Potentials

We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The "atomic body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic basis and are constructed to preserve the symmetry of the potential ener...

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Bibliographic Details
Published inarXiv.org
Main Authors Cas van der Oord, Dusson, Geneviève, Csanyi, Gabor, Ortner, Christoph
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.10.2019
Subjects
Artificial neural networks
Basis functions
Decomposition
Invariants
Kernels
Permutations
Polynomials
Potential energy
Regularization
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Summary:We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The "atomic body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic basis and are constructed to preserve the symmetry of the potential energy function with respect to rotations and permutations. In contrast to kernel based and artificial neural network models, the explicit decomposition of the total energy as a sum of atomic body-ordered terms allows to keep the dimensionality of the fit reasonably low, up to just 10 for the 5-body terms. The explainability of the potential is aided by this decomposition, as the low body-order components can be studied and interpreted independently. Moreover, although polynomial basis functions are thought to extrapolate poorly, we show that the low dimensionality combined with careful regularisation actually leads to better transferability than the high dimensional, kernel based Gaussian Approximation Potential.
ISSN:2331-8422