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_ip, 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 study would enable principled selection and optimization of nonlinear embeddings, rather than relying on ad hoc choices.

References

A full systematic study of the number, exponents, etc. of the terms that enter F is yet to be reported, and it is likely that there is some scope for optimizing nonlinear ACE models in this regard.

— Hyperparameter Optimization for Atomic Cluster Expansion Potentials  (2408.00656 - Toit et al., 2024) in Methods, Atomic Cluster Expansion subsection (end)

However, it remains unclear to what extent such high-order correlations arising from the nonlinear transformation of edge features contribute to its accuracy and transferability.

— Generalizing Abell-Tersoff bond-order potential with explicit high-order many-body correlations for robust extrapolation of potential energy surfaces  (2608.22933 - Kohata, 24 Aug 2026) in Appendix, Section “Effective body order of Abell–Tersoff bond-order potential”