Systematic study of nonlinear ACE embedding terms

Conduct a full systematic study of the number of atomic property terms and their exponents, as well as related parameters of the terms entering the nonlinear embedding function F in the Atomic Cluster Expansion energy expression ε_i = F(φ_i^(1), ..., φ_i^(P)), to characterize their influence and to guide optimization of nonlinear ACE interatomic potentials.

Background

In the Atomic Cluster Expansion (ACE) framework, the atomic energy can be expressed as a nonlinear function F of multiple atomic "properties" φ_i^p, allowing flexible, Finnis–Sinclair-like or more complex embeddings. Prior work has shown that increasing the number of properties (P) and choosing specific functional forms can improve accuracy for certain systems with modest computational overhead.

However, the field lacks a comprehensive, systematic investigation of how the number of properties, their exponents, and related term parameters inside F affect accuracy, robustness, and efficiency of ACE models across systems. Establishing such a paper would enable principled selection and optimization of nonlinear embeddings, rather than relying on ad hoc choices.