A Critical Evaluation of Kolmogorov–Arnold Networks for Shear-Wave Slowness Prediction from Well Logs

Abstract

Kolmogorov–Arnold networks (KANs) are increasingly applied to well-log and reservoir problems, but their evaluation protocols rarely control preprocessing leakage, replicate comparators across seeds, or test depth-shifted generalization. This study evaluates a KAN for predicting shear-wave slowness from seven conventional logs and two engineered proxies on a public, depth-indexed dataset of 1904 records, benchmarked against six model families under a leakage-free protocol with five-seed replication. On the random split, KAN is competitive (R2 ≈ 0.99) but not the best model: gradient-boosted ensembles and a multilayer perceptron score higher. Once adjacent-sample leakage is removed by blocked depth cross-validation, every family degrades sharply, and in a shallow-to-deep test with matched preprocessing, hyperparameters, and seeds, KAN loses most of its accuracy (an 8-fold RMSE increase) while compact symbolic regression retains the highest mean accuracy. Edge-level symbolic templates fit individual KAN edges well, but no template identity is stable across seeds, so edge fits serve as diagnostics rather than recovered physical laws. These results separate interpolation accuracy from depth generalization and indicate the evidence—multiwell blocked validation and calibrated uncertainty—required before KAN-based log reconstruction can be considered reliable.