Data–Model Synergy in Asphalt Viscoelasticity: A Fractional-Order Physics-Informed Neural Network Framework with Depth-Resolved Heterogeneity Decoupling

This study introduces a physics-informed deep learning framework for modeling the viscoelastic behavior of asphalt binders using a fractional-order Kelvin–Voigt series model embedded within a physics-informed neural network (PINN). By enforcing Kramers–Kronig constraints and integrating depth-frequency-dependent input features, the proposed fractional-order constitutive PINN (FO-PINN) framework captures broadband dynamic modulus behavior with high accuracy (global R 2 > 0.96 ). A unique material embedding strategy enables the network to generalize across different binder types while preserving material-specific characteristics. Sensitivity analysis reveals that long-term viscosities ( η 2 , η 3 ) and the fractional derivative order ( α ) dominate the rheological response, reflecting the multiscale nature of asphalt microstructure. The model demonstrates superior performance compared to conventional identification methods in terms of accuracy, generalizability, and physical consistency. Furthermore, its capability to decode depth-resolved viscoelastic gradients and support cross-material parameter estimation highlights its potential as a foundational tool for digital twins of pavement systems. These findings promote the adoption of physics-constrained machine learning in civil material informatics and infrastructure resilience assessment.