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

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 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.

References in corpus (18)

• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• On representing chemical environments
• Comparing molecules and solids across structural and alchemical space
• Machine Learning Unifies the Modelling of Materials and Molecules
• Machine-learning based interatomic potential for amorphous carbon
• Machine Learning of Molecular Electronic Properties in Chemical Compound Space
• AiiDA: Automated Interactive Infrastructure and Database for Computational Science
• Competing quantum effects in the dynamics of a flexible water model
• A First-Principles Approach to Insulators in Finite Electric Fields
• Machine Learning Energies of 2 M Elpasolite (ABC${}_2$D${}_6$) Crystals
• i-PI: A Python interface for ab initio path integral molecular dynamics simulations
• Accurate Interatomic Force Fields via Machine Learning with Covariant Kernels
• Transferable atomic multipole machine learning models for small organic molecules
• A high-throughput ab initio review of platinum-group alloy systems
• Learning molecular energies using localized graph kernels
• Solvent Fluctuations and Nuclear Quantum Effects Modulate the Molecular Hyperpolarizability of Water
• Second-Harmonic Scattering as a Probe of Structural Correlations in Liquids
• Structural Simplicity as a Restraint on the Structure of Amorphous Silicon

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• Unified theory of atom-centered representations and message-passing machine-learning schemes
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• REANN: A PyTorch-based End-to-End Multi-functional Deep Neural Network Package for Molecular, Reactive and Periodic Systems
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• Improving accuracy of interatomic potentials: more physics or more data? A case study of silica
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