Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems.

By Andrea Grisafi, David M. Wilkins, Gábor Csányi, Michele Ceriotti. 2017

241 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Materials Chemistry

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Citations in the corpus

SE(3)-equivariant prediction of molecular wavefunctions and electronic densities (2021, background): “Datasets for all molecules are taken from [33], with the exception of aspirin, for which geometries were sampled from the MD17 dataset [5] (more details on the datasets, training procedure, and hyperparameter settings can be found in Sections F and G of the supplement).”
The MLIP package: moment tensor potentials with MPI and active learning (2020, methodology): “Probably because of this MTP together with GAP showed excellent accuracy in recent cheminformatics benchmark test [54] and interatomic potential test [82]; in the latter MTP showed also a very good balance between accuracy and computational eﬃciency when compared against other machine-learning poten”
A high-bias, low-variance introduction to Machine Learning for physicists (2018, unknown): “For example, recent works have used ideas from ML to investigate disparate topics such as disordered materials and glasses (Schoenholz, 2017), electronic structure calculations (Grisafi et al., 2017), designing and analyzing quantum materials by integrating ML with existing techniques such as Dynami”