KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes

Tool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolmogorov–Arnold Networks (KANs) to address the trade-off between accuracy and interpretability in lathe tool wear modeling. Three KAN variants (KAN-A, KAN-B, and KAN-C) with varying complexities are proposed, using feed rate, depth of cut, and cutting speed as input variables to model flank wear. The proposed KAN-based framework generates interpretable mathematical expressions for tool wear, enabling transparent decision-making. To evaluate the performance of KANs, this research systematically compares prediction errors, topological evolutions, and mathematical interpretations of derived symbolic formulas. For benchmarking purposes, MLP-A, MLP-B, and MLP-C models are developed based on the architectures of their KAN counterparts. A comparative analysis between KAN and MLP frameworks is conducted to assess differences in modeling performance, with particular focus on the impact of network depth, width, and parameter configurations. Theoretical analyses, grounded in the Kolmogorov–Arnold representation theorem and Cybenko’s theorem, explain KANs’ ability to approximate complex functions with fewer nodes. The experimental results demonstrate that KANs exhibit two key advantages: (1) superior accuracy with fewer parameters compared to traditional MLPs, and (2) the ability to generate white-box mathematical expressions. Thus, this work bridges the gap between empirical models and black-box machine learning in manufacturing applications. KANs uniquely combine the adaptability of data-driven methods with the interpretability of physics-based models, offering actionable insights for researchers and practitioners.