A Post-Hoc Interpretable Depth-Sequential Residual Kolmogorov-Arnold Network-Long Short-Term Memory Framework for Fracture Density Identification in Volcanic Reservoirs

Summary

Identifying natural fractures in heterogeneous volcanic reservoirs using conventional well logs is challenging due to complex log responses. Although deep learning models improve prediction accuracy, their black-box nature limits geological interpretability. To address this issue, a hybrid deep learning architecture, termed the depth-sequential residual Kolmogorov-Arnold network (KAN)-long short-term memory (LSTM) framework (DRK-LSTM), is proposed. The method uses a two-stage modeling procedure. First, an independent cross-validation protocol is applied, in which feature selection is conducted using an integrated gradients (IG) algorithm based on a surrogate KAN. Subsequently, the selected sequence data are used to train the DRK-LSTM model, which combines KAN and LSTM units in a residual structure to capture underlying sequential relationships, thereby reducing pointwise errors and mitigating the nonuniqueness of log responses caused by strong heterogeneity. To improve interpretability, post-hoc symbolic expressions are extracted from the surrogate model to represent the relationships between well logs and fracture density. The proposed method is tested using well data from Carboniferous volcanic reservoirs in the Junggar Basin. Validation results show that the DRK-LSTM achieves an average coefficient of determination (R2) of 0.9351 ± 0.0027 and an average root mean square error (RMSE) of 0.1866 ± 0.0044, outperforming all 13 baseline models. Furthermore, the extracted symbolic expressions provide an interpretable approximation of the nonlinear log responses.