<p>Automatic lithology identification based on well logs plays a crucial role in oil and gas resource exploration. Traditional manual interpretation and statistical methods are time-consuming, subjective, and prone to bias, while existing deep learning (DL) methods suffer from fixed activation functions and limited multi-scale feature extraction. To address these issues, we propose a novel wavelet-based Kolmogorov-Arnold network for well logs (LogWKAN) that replaces static activation functions with learnable wavelet basis functions, enabling dynamic adaptation to logging data patterns. Unlike conventional DL architectures, LogWKAN integrates a wavelet-based Kolmogorov-Arnold (WKA) module to jointly capture high-frequency details (e.g., lithological boundaries) and low-frequency trends. Experiments on clastic and volcanic reservoirs demonstrate the superiority of LogWKAN. It achieves performance improvements of 2.35–9.07% on two clastic reservoirs and 2.24–7.54% on the volcanic reservoir compared to four leading families of DL methods—convolutional neural networks, transformers, multi-layer perceptrons, and recurrent neural networks. Case studies confirm its robustness on imbalanced datasets and adaptability to diverse geological settings. By resolving the trade-off between interpretability and identification performance, LogWKAN offers a promising framework for lithology identification.</p>