From black boxes to formulas: interpretable Kolmogorov-Arnold networks for HF-3c-to-DFT descriptor prediction

Converting inexpensive HF-3c descriptors into density functional theory (DFT) quality values is attractive for high-throughput screening, but only if the correction is known. We learn such corrections for six descriptors (Gibbs, electronic and enthalpy energies, the entropy term TS, dipole moment and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap) of 1031 cyclic supramolecular structures with Kolmogorov-Arnold networks (KANs) fed by the six HF-3c values alone. Against conventional models retrained on the same inputs, ten-seed KAN ensembles (114-252 parameters per network) are competitive and most accurate for four of six targets, although the cross-validated differences are not statistically significant. On the test partition of a previous benchmark, they reach the lowest error among eleven models for every target, although these models used different inputs. Each target admits an explicit, empirical closed-form expression. Within this data set the three energies obey DFT ≈ 1.0121 · HF + C, while feature attribution shows that each non-energy property is dominated by its own HF-3c analogue.

HF-3c descriptors and their B3LYP-D4/def2-TZVP counterparts were taken unchanged from a published data set, together with its original 90:10 train/test split. KANs were built with the pykan library in Python, using cubic B-spline edge functions optimized with the L-BFGS algorithm, and were converted into closed-form expressions by symbolic regression. Feature attribution used the KAN 2.0 framework. Conventional regressors were retrained on identical inputs and compared by repeated cross-validation. An interactive Streamlit application applies the models and formulas to single compounds or comma-separated values (CSV) batches.