Interatomic potentials drop the single cutoff: MCSA stacks three radial scales and cuts thermal-conductivity error by 13.7%

Radial interactions in an interatomic potential are no longer tied to a single cutoff radius; radial kernels at several spatial scales are superposed inside one equivariant message-passing operation. Earlier SO(3)-equivariant message passing used one cutoff radius for all edges, which under a scale-consistent radial parameterization supplies only one characteristic spatial-frequency scale. On the in-distribution MPtrj test split and the out-of-distribution Alexandria set, adding MCSA lowers energy, force and stress errors for all three backbones Nequix, Eqnorm and EquiformerV3; EquiformerV3+MCSA reduces out-of-distribution energy, force and stress mean absolute errors by 8.1%, 5.5% and 5.1%.

The extra cost of multiple cutoffs lands mainly on radial weights, while the angular tensor product is computed once per edge. Evaluating Clebsch–Gordan tensor products separately for every cutoff branch makes the number of angular contractions grow with the number of cutoffs. Exploiting the compact support of radial kernels, cutoff-dependent radial weights are summed before the angular tensor product, so angular contractions drop from growing with the cutoff count to one per edge; in the ablation, the three-cutoff configuration raises per-material inference latency from 47 ms to 51 ms.

Multi-scale radial representation improves not only energy and force but also properties sensitive to second derivatives of the potential energy surface. Phonon dispersion and lattice thermal conductivity depend on second- and third-order force constants and are sensitive to local-curvature errors of the potential energy surface. On PhononDB-103, Nequix+MCSA lowers the symmetric relative mean error of thermal conductivity from 0.487 to 0.420, a 13.7% relative reduction, while average per-material time rises from 1.107 to 1.136 minutes, an overhead below 3%.

The demonstrated scope is energy, force and stress prediction on SO(3)-equivariant message-passing backbones, plus phonon dispersion, lattice thermal conductivity, layered Mo–S structures and 300 K, 100 ps NVE molecular dynamics; cutoff radii are supplied in advance rather than learned by the model.

Cutoff radii currently rely on predefined radial scales that may not be optimal for every chemical environment; the authors list adaptive cutoff scheduling and cross-scale nonlinear coupling as future directions. The ablation shows no further gain beyond three cutoffs, indicating that choosing complementary scales matters more than simply adding cutoffs.