KAN-Based Tool Wear Modeling with Adaptive Complexity and Symbolic Interpretability in CNC Turning Processes
Source abstract
Abstract
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.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Manufacturing Process and Optimization · Machine Learning in Materials Science · Advanced machining processes and optimization
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Mechanical Engineering and Automation, Beihang University, Beijing 102206, China
Jiangxi Research Institute, Beihang University, Nanchang 330096, China
Jiangxi Province Key Laboratory of High-End CNC Machine Tools, Jiangxi Research Institute, Beihang University, Nanchang 330096, China
Funding
Jiangxi Province Key Laboratory of High-end CNC Machine Tools
References (36)
Show source-provided references
1. A Milling Tool Wear Predicting Method with Processing Generalization Capability10.1016/j.jmapro.2024.05.022 ↗
2. Val, S., Lambán, M.P., Lucia, J., and Royo, J. (2024). Analysis and Prediction of Wear in Interchangeable Milling Insert Tools Using Artificial Intelligence Techniques. Appl. Sci., 14.10.20944/preprints202411.1647.v1 ↗
3. Tool Wear Segmentation in Blanking Processes with Fully Convolutional Networks Based Digital Image Processing10.1016/j.jmatprotec.2023.118270 ↗
4. Zhang, H., Jiang, S., Gao, D., Sun, Y., and Bai, W. (2024). A Review of Physics-Based, Data-Driven, and Hybrid Models for Tool Wear Monitoring. Machines, 12.10.3390/machines12120833 ↗
5. Assessment of Cutting Tool Wear Using a Numerical FEM Simulation Model10.1088/1742-6596/2712/1/012021 ↗
6. Xie, X., Huang, M., Sun, W., Li, Y., and Liu, Y. (2023). Intelligent Tool Wear Monitoring Method Using a Convolutional Neural Network and an Informer. Lubricants, 11.10.3390/lubricants11090389 ↗
7. Toward Practical Tool Wear Prediction Paradigm with Optimized Regressive Siamese Neural Network10.1016/j.aei.2023.102200 ↗
8. Shah, R., Jaramillo, R., Thomas, G., Rayhan, T., Hossain, N., Kchaou, M., Profito, F.J., and Rosenkranz, A. (2025). Artificial Intelligence and Machine Learning in Tribology: Selected Case Studies and Overall Potential. Adv. Eng. Mater., 2401944.10.1002/adem.202401944 ↗
9. Tool Wear Prediction Combining Global Feature Attention and Long Short-Term Memory Network10.46604/peti.2024.14201 ↗
10. Wang, K., Wang, A., and Wu, L. (2024). Research on Tool Wear Monitoring Technology Based on Variational Mode Decomposition and Back Propagation Neural Network Model. Sensors, 24.10.3390/s24248107 ↗
11. Demystifying the Black Box: An Overview of Explainability Methods in Machine Learning
12. In-Process Tool Wear Prediction System Based on Machine Learning Techniques and Force Analysis10.1016/j.procir.2018.08.253 ↗
13. An In-Process Tool Wear Assessment Using Bayesian Optimized Machine Learning Algorithm10.1007/s12008-023-01270-3 ↗
14. On the Readiness of Scientific Data Papers for a Fair and Transparent Use in Machine Learning10.1038/s41597-025-04402-4 ↗
15. Learning from Models beyond Fine-Tuning10.1038/s42256-024-00961-0 ↗
16. Liu, Z., Wang, Y., Vaidya, S., Ruehle, F., Halverson, J., Soljačić, M., Hou, T.Y., and Tegmark, M. (2025). KAN: Kolmogorov-Arnold Networks. arXiv.
17. Liu, Z., Ma, P., Wang, Y., Matusik, W., and Tegmark, M. (2024). KAN 2.0: Kolmogorov-Arnold Networks Meet Science. arXiv.
18. Wang, Z., Zainal, A., Siraj, M.M., Ghaleb, F.A., Hao, X., and Han, S. (2025). An Intrusion Detection Model Based on Convolutional Kolmogorov-Arnold Networks. Sci. Rep., 15.10.1038/s41598-024-85083-8 ↗
19. fKAN: Fractional Kolmogorov–Arnold Networks with Trainable Jacobi Basis Functions10.1016/j.neucom.2025.129414 ↗
20. Reinhardt, E., Ramakrishnan, D., and Gleyzer, S. (2025). SineKAN: Kolmogorov-Arnold Networks Using Sinusoidal Activation Functions. Front. Artif. Intell., 7.10.3389/frai.2024.1462952 ↗
21. Kolmogorov–Arnold-Informed Neural Network: A Physics-Informed Deep Learning Framework for Solving Forward and Inverse Problems Based on Kolmogorov–Arnold Networks10.1016/j.cma.2024.117518 ↗
22. Shuai, H., and Li, F. (2024). Physics-Informed Kolmogorov-Arnold Networks for Power System Dynamics. arXiv.10.1109/OAJPE.2025.3529928 ↗
23. Livieris, I.E. (2024). C-KAN: A New Approach for Integrating Convolutional Layers with Kolmogorov–Arnold Networks for Time-Series Forecasting. Mathematics, 12.10.3390/math12193022 ↗
24. Firsov, N., Myasnikov, E., Lobanov, V., Khabibullin, R., Kazanskiy, N., Khonina, S., Butt, M.A., and Nikonorov, A. (2024). HyperKAN: Kolmogorov–Arnold Networks Make Hyperspectral Image Classifiers Smarter. Sensors, 24.10.3390/s24237683 ↗
25. Jiang, C., Li, Y., Luo, H., Zhang, C., and Du, H. (2025). KansNet: Kolmogorov–Arnold Networks and Multi Slice Partition Channel Priority Attention in Convolutional Neural Network for Lung Nodule Detection. Biomed. Signal Process. Control., 103.10.1016/j.bspc.2024.107358 ↗
26. Kolmogorov–Arnold Recurrent Network for Short Term Load Forecasting across Diverse Consumers10.1016/j.egyr.2024.12.038 ↗
27. Tang, Z., Hou, X., Wang, X., and Zou, J. (2024). A Cross-Working Condition-Bearing Diagnosis Method Based on Image Fusion and a Residual Network Incorporating the Kolmogorov–Arnold Representation Theorem. Appl. Sci., 14.10.3390/app14167254 ↗
28. Cabral, T.W., Gomes, F.V., De Lima, E.R., Filho, J.C.S.S., and Meloni, L.G.P. (2024). Kolmogorov–Arnold Network in the Fault Diagnosis of Oil-Immersed Power Transformers. Sensors, 24.10.3390/s24237585 ↗
29. Peng, Y., Wang, Y., Hu, F., He, M., Mao, Z., Huang, X., and Ding, J. (2024). Predictive Modeling of Flexible EHD Pumps Using Kolmogorov–Arnold Networks. Biomim. Intell. Robot., 4.10.1016/j.birob.2024.100184 ↗
30. Accurately Models the Relationship Between Physical Response and Structure Using Kolmogorov–Arnold Network10.1002/advs.202413805 ↗
31. Predicting Chlorophyll- a Concentrations in the World’s Largest Lakes Using Kolmogorov-Arnold Networks10.1021/acs.est.4c11113 ↗
32. KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Search10.1140/epjqt/s40507-024-00289-z ↗
33. Liu, C.Z., Zhang, Y., Qin, L., and Liu, Y. (2024). Kolmogorov–Arnold Finance-Informed Neural Network in Option Pricing. Appl. Sci., 14.10.3390/app142411618 ↗
34. MP-KAN: An Effective Magnetic Positioning Algorithm Based on Kolmogorov-Arnold Network10.1016/j.measurement.2024.116248 ↗
35. Real-Time Tool Wear Monitoring and Multi-Step Forward Prediction Based on Multi-Information Fusion10.1088/1361-6501/ada4cf ↗
36. Kupczyk, M., Leleń, M., Józwik, J., and Tomiło, P. (2024). Modeling Material Machining Conditions with Gear-Shaper Cutters with TiN0.85-Ti in Adhesive Wear Dominance Using Machine Learning Methods. Materials, 17.10.3390/ma17225567 ↗