Optimal radial basis choice for CACE/ACE-style ML interatomic potentials

Determine the optimal choice of radial basis functions for the CACE edge basis R_{n,cl}(r), including the functional family (e.g., trainable Bessel functions with smooth cutoff versus alternative bases), parametrization, and coupling to angular momentum l and edge channel c, that maximizes learning efficiency while maintaining accuracy and stability in machine learning interatomic potentials.

Background

In the CACE framework, the edge basis combines a radial component R_{n,cl}(r), an angular component L, and an edge-type component T. The authors currently employ a set of trainable Bessel functions multiplied by a smooth cutoff, with distinct radial bases coupled to the total angular momentum l and the edge channel c.

The paper emphasizes that engineering decisions, including dataset normalization and internal normalization, affect training outcomes. Importantly, the authors note that the choice of radial basis has a significant impact on learning efficiency, but the optimal selection is not yet established.