KEN embeds 2D convolutional kernels in an E(3)-equivariant potential: training energy error reaches 6.93 meV/atom, but test-set force error stays above MACE

An interatomic potential no longer starts only from nuclear geometry: it takes electronic spin-interaction matrices as a second input path, so one geometric arrangement can map to distinct electronic and spin states. Earlier E(3)-equivariant graph neural networks built potential energy surfaces from 3D Cartesian coordinates and static chemical identities alone, and that coordinate-only description becomes ill-posed in strongly correlated materials where electronic, magnetic or spin degrees of freedom decouple from geometry. On the HE26 actinide dataset, KENJI reaches a training bonding-energy mean absolute error of 6.93 meV/atom and root-mean-square error of 13.28 meV/atom, against 44.7 and 117.3 meV/atom for MACE-osaka26; its training force mean absolute error is 34.10 meV/Å versus 26.30 meV/Å for MACE-osaka26.

The implementation lays each structure's spin information onto a multichannel 2D grid, extracts local magnetic environments with 3×3 convolutions, and injects the result into the scalar channels of the equivariant graph network. Because 2D convolution mixes spatial neighbors it does not commute with arbitrary atom reordering, so inputs first pass through a canonicalization map that sorts by element species, distance from the centroid, then original index. After a random permutation of a six-atom (AmO2)2 structure, energy invariance and force equivariance hold to single-precision floating-point limits; across 648 test structures for magnetic moments, KENJI with 50% perturbed reference inputs reaches R² = 0.961 and RMSE 0.365 μB, against CHGNet's RMSE of 0.472 μB.

The demonstrated scope is training and independent testing on the HE26 actinide dataset, plus Birch–Murnaghan equation-of-state fits, a magnetic-moment comparison, 300 K microcanonical dynamics and 1400 K Langevin dynamics with this potential; the authors state that quantitative comparison against AIMD is deferred until the training set is augmented with close-contact, high-force configurations.

The authors report that periodic CmO2 peaks at an energy drift of 6.186 meV/atom/ps at Δt = 0.5 fs, which falls below 0.18 meV/atom/ps after retraining on a 1565-structure AcHE26 subset, and attribute this to training-data coverage rather than an architectural defect; at 1400 K the radial distribution functions show a spurious short-range feature near 1.0–1.5 Å, which the authors attribute to a training set of near-equilibrium configurations that does not cover the short-range repulsive wall, so no quantitative AIMD benchmark is attempted.