Recursive evaluation and iterative contraction of N-body equivariant features

Area of Science:

• Materials Science
• Computational Chemistry
• Machine Learning

Background:

• Representing atomic structures for machine learning often uses N-point correlations.
• Low-order correlations are insufficient for a complete atomic environment representation.
• High-order correlations become computationally complex due to exponential growth.

Purpose of the Study:

• To develop an efficient method for generating complete, symmetry-adapted representations for atomistic machine learning.
• To address the challenge of designing concise and effective representations using high-order correlations.
• To enable systematically improvable representations for atomic environments.

Main Methods:

• Exploiting recursion relations between equivariant features of different orders.
• Generalizing N-body invariants to include symmetries of improper rotations.
• Automatic selection of the most expressive feature combinations at each order.

Main Results:

• Efficient computation of high-order correlation terms.
• A framework for generating systematically improvable representations.
• Enhanced completeness and symmetry adaptation in atomic representations.

Conclusions:

• The proposed approach provides a practical framework for advanced atomistic machine learning.
• Efficiently computable, high-order equivariant features offer a complete representation of atomic environments.
• This method facilitates the development of more accurate and robust machine learning models for materials science.