WISP: Learning spin-resolved electron localization from atomic environments

The electron localization function (ELF) reveals bonding and interstitial localization in crystals, but obtaining it usually requires an electronic-structure calculation. Here we develop WISP, Wavefunction-free Inference of Scalar Properties, in which a nonlinear decoder predicts spin-resolved ELF from encoded atomic environments at arbitrarily chosen positions. Signed site moments supply the magnetic information, and two evaluations of a shared network with opposite moments enforce exact spin-channel exchange. We obtain a structure-weighted paired-channel mean absolute error (MAE) of 0.01065 for the model with far-field input on the complete grids of 21,922 held-out structures from a frozen MatPES-derived PBE dataset. With moments predicted from geometry by a separate network, we obtain an average-field MAE of 0.00974. The predictions retain the spin contrast of the magnetic examples and resolve the interstitial localization for electride screening. We propose using predicted ELF to select structures for further electronic-structure calculations.