Recursive evaluation and iterative contraction of $N$-body equivariant features

Abstract

Mapping an atomistic configuration to an $N$-point correlation of a field associated with the atomic positions (e.g. an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible $N$-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different orders (generalizations of $N$-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically-improvable, symmetry adapted representations for atomistic machine learning.

References in corpus (6)

• A Spectral Analysis Method for Automated Generation of Quantum-Accurate Interatomic Potentials
• Machine Learning Unifies the Modelling of Materials and Molecules
• Symmetry-Adapted Machine-Learning for Tensorial Properties of Atomistic Systems
• Understanding molecular representations in machine learning: The role of uniqueness and target similarity
• Accurate Force Field for Molybdenum by Machine Learning Large Materials Data
• Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials

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• Learning electron densities in the condensed phase
• REANN: A PyTorch-based End-to-End Multi-functional Deep Neural Network Package for Molecular, Reactive and Periodic Systems