Wigner kernels: body-ordered equivariant machine learning without a basis

Filippo Bigi, Sergey Pozdnyakov, Michele Ceriotti

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Keywords: Geometric machine learning, kernel methods, chemistry, molecular modeling

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TL;DR: A kernel formulation of equivariant machine learning that accurately approximates the properties of molecules and materials

Abstract:

Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different approaches that have been pursued, the description of local atomic environments in terms of their discretized neighbor densities has been used widely and very successfully.
We propose a novel density-based method which involves computing "Wigner kernels''. These are fully equivariant and body-ordered kernels that can be computed iteratively with a cost that is independent of the basis used to discretize the density and grows only linearly with the maximum body-order considered. This is in marked contrast to feature-space models, whose number of terms and computational cost scale exponentially with increasing order of correlations.
We present several examples of the accuracy of models based on Wigner kernels in chemical applications, for both scalar and tensorial targets, reaching state-of-the-art accuracy on the popular QM9 benchmark dataset. We discuss the broader relevance of these findings to equivariant geometric machine-learning.

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Submission Number: 7657