Source-linked AI summary
Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
Andrea Grisafi, David M. Wilkins, Gábor Csányi, Michele Ceriotti
TL;DR
Tensorial-property learning must transform covariantly under rotations rather than remain invariant. The paper introduces symmetry-adapted GPR and λ-SOAP kernels, demonstrating learning across water systems from isolated molecules to condensed phase.
Problem
Scalar-property models exploit rotational and permutational invariance, but tensorial properties require appropriate geometric transformations under reference-frame rotations.
Method
The paper introduces a GPR framework for arbitrary-order tensorial properties and constructs SOAP-based kernels that encode their rotational covariance.
Results
The approach learns electric response tensors for water monomers, oligomers, charged complexes, and condensed-phase configurations, with errors below 5% for the Zundel cation and below 0.01 a.u. for condensed-phase dielectric components.
Takeaways & Limitations
Symmetry-adapted tensor kernels provide a generally applicable route to learning anisotropic properties from isolated molecules through condensed phases.
Takeaways & Limitations
The scalar kernel must be independent of the absolute reference frame, although it may depend on the relative orientation of the configurations.
Abstract
from arXiv · showhide
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 can be used to perform machine-learning of tensorial properties of arbitrary rank 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 (SOAP) 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 electrical response of water oligomers of increasing complexity, from the isolated molecule to the condensed phase.