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Description
This paper introduces a novel approach to modeling the viscoelastic behavior of materials by leveraging Kolmogorov-Arnold Networks (KANs) to generate interpretable, closed-form expressions with minimal parameters. Accurate prediction of viscoelastic responses is essential in applications ranging from asphalt binders to polymeric materials. However, traditional mechanical and mathematical models often require extensive parameterization and careful initialization, leading to optimization challenges and potential convergence to local minima. The present approach employs the KAN architecture, which is grounded in the Kolmogorov-Arnold representation theorem. Unlike conventional multilayer perceptrons with fixed activation functions, KANs utilize learnable activation functions on network edges, enabling a continuous search in function space that facilitates symbolic regression and yields explicit mathematical formulas offering physical insight. Applied to master curve construction for storage modulus, loss modulus, and phase angle across a range of viscoelastic materials, including neat and modified asphalt binders, asphalt mastics, and polymers such as PMMA, ECOVIO, and PLA, the KAN model demonstrates exceptional performance. With a minimal [1–2–1] architecture comprising only 13 parameters, the model achieved Summation of Square of Relative Errors (SSRE) values as low as 0.12–0.51 for various asphalt binders (with an average of 0.27). In contrast, the highly parameterized Generalized Maxwell Model (GM20), which utilizes 40 parameters, yielded SSRE values averaging around 1.04, depicting KAN’s superior accuracy and efficiency. KANs also excel in modeling phase angle master curves, capturing intricate behaviors such as plateaus and inflection points with high precision without overfitting. For polymeric materials, the advantages of the KAN approach are even more pronounced. KAN variants significantly reduced average relative errors in the storage and loss moduli. For instance, while traditional models such as the Generalized Fractional Maxwell (GFM) and Fractional Zener (FZ) models recorded average errors in the range of 4.1–22.5% for polymers, KAN models reduced these errors to as low as approximately 0.6–4.9%. This reduction in error, achieved with far fewer parameters, highlights KAN’s capability to effectively capture complex frequency-dependent behaviors. In summary, the KAN-based model delivers superior predictive accuracy and computational efficiency while providing interpretable symbolic formulas, making it a transformative tool for viscoelastic characterization and material design in diverse engineering applications.
