Unified theory of atom-centered representations and message-passing machine-learning schemes

Area of Science:

• Materials Science
• Computational Chemistry
• Machine Learning

Background:

• Data-driven methods require effective descriptions of atomic arrangements in molecules and crystals.
• Current models often focus on atom-centered environments or message-passing interactions.
• Atom-centered density correlations (ACDC) provide a basis for symmetry-adapted expansions.

Purpose of the Study:

• To generalize the ACDC framework to incorporate multi-centered information.
• To develop a unified approach for atom-centered and message-passing machine learning schemes.
• To provide a complete linear basis for regressing symmetric functions of atomic coordinates.

Main Methods:

• Generalization of the atom-centered density correlations (ACDC) framework.
• Inclusion of multi-centered information into structural representations.
• Development of a basis for regressing symmetric functions of atomic coordinates.

Main Results:

• A generalized ACDC framework capable of handling multi-centered atomic environments.
• A unified approach that systematizes both atom-centered and message-passing machine learning schemes.
• A complete linear basis for representing atomic structures and predicting properties.

Conclusions:

• The generalized framework provides a coherent foundation for diverse machine learning approaches in materials science.
• This work unifies and extends existing methods for structural representation.
• Enables more systematic development and understanding of invariant and equivariant machine learning models.