RACE: A Modular and Interpretable Radial-Angular Correlation Descriptor for Atomistic Machine Learning

Atomistic machine learning (ML) representations involve trade-offs among predictive accuracy, physical interpretability, descriptor dimensionality, and computational cost. Here, we introduce the Radial-Angular Correlation Descriptor (RACE), a modular representation constructed from radial distributions, angular distributions, and an explicit joint radial-angular map. Chemical identity is incorporated through interchangeable scalar or multichannel weighting functions rather than through a mandatory set of element-pair channels. We evaluate RACE against conventional smooth overlap of atomic positions (SOAP), compressed SOAP-μ2, atom-centered symmetry functions (ACSF), and a fixed-basis atomic cluster expansion (ACE) representation using common train-test partitions, training-only feature selection, repeated evaluations, and uncertainty estimates. RACE provides useful predictive accuracy across structurally and chemically diverse systems, but it does not uniformly outperform the alternative representations. Compressed SOAP is particularly accurate for the chemically heterogeneous benchmarks, whereas explicit composition features are required for robust generalization across broad Materials Project chemical spaces. Direct ablation of the radial, angular, and joint channels further shows that the incremental value of the joint radial-angular term is system dependent. The principal practical characteristics of RACE are therefore its transparent component structure, configurable chemical encoding, descriptor dimension independent of the number of species in its scalar-weighted form, and low peak memory during descriptor generation. RACE is consequently presented as a simple and manipulable structural representation that complements, rather than universally replaces, systematic density-correlation descriptors.