Wigner kernels: Body-ordered equivariant machine learning without a basis.

Area of Science:

• Computational chemistry
• Materials science
• Machine learning

Background:

• Machine learning models using point-cloud representations are vital for atomic-scale descriptions of molecules and materials.
• Discretized neighbor densities are a common and successful approach for describing local atomic environments.

Purpose of the Study:

• To propose a novel density-based machine learning method using Wigner kernels.
• To demonstrate the efficiency and accuracy of Wigner kernels for chemical applications.

Main Methods:

• Computing fully equivariant and body-ordered Wigner kernels.
• Iterative computation with cost independent of basis and linear with body-order.
• Representing the infinite-width limit of feature-space models.

Main Results:

• Wigner kernels achieve accuracy competitive with state-of-the-art deep learning architectures.
• Demonstrated accuracy for both scalar and tensorial targets in chemical applications.
• Computational cost scales linearly with body-order, unlike exponential scaling of other models.

Conclusions:

• Wigner kernels offer an efficient and accurate alternative for atomic-scale machine learning.
• The method has broad relevance to equivariant geometric machine learning.
• This work advances density-based approaches in computational chemistry and materials science.