Abstract
Statistical learning methods show great promise in providing an accurate prediction of materials and molecular properties, while minimizing the need for computationally demanding electronic structure calculations. The accuracy and transferability of these models are increased significantly by encoding into the learning procedure the fundamental symmetries of rotational and permutational invariance of scalar properties. However, the prediction of tensorial properties requires that the model respects the appropriate geometric transformations, rather than invariance, when the reference frame is rotated. We introduce a formalism that extends existing schemes and makes it possible to perform machine learning of tensorial properties of arbitrary rank, and for general molecular geometries. To demonstrate it, we derive a tensor kernel adapted to rotational symmetry, which is the natural generalization of the smooth overlap of atomic positions kernel commonly used for the prediction of scalar properties at the atomic scale. The performance and generality of the approach is demonstrated by learning the instantaneous response to an external electric field of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.
Original language  English 

Article number  036002 
Journal  Physical Review Letters 
Volume  120 
Issue number  3 
DOIs  
Publication status  Published  19 Jan 2018 
Keywords
 Machine Learning
 Symmetry
 Gaussian Process Regression
 Coupled Cluster Theory
 Dielectric Response
ASJC Scopus subject areas
 Physics and Astronomy(all)
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David Wilkins
 School of Mathematics and Physics  ViceChancellor Illuminate Fellow
 Atomistic Simulation Centre (ASC)
Person: Research