We present a hybrid modeling approach combining Physics-Informed Neural Networks (PINNs) with symbolic regression to discover interpretable constitutive laws for waxy crude oils. Guided by the structure of the Fractal Isotropic Kinematic Hardening (FIKH) and SoFA models, we use flow curve data across temperatures and wax volume fractions to train PINNs under steady-state conditions. Symbolic regression tools—AI Feynman, NeSymReS, and PySR—are then applied to extract closed-form stress expressions that capture key nonlinear rheological features. These expressions are compared to classical models such as Herschel–Bulkley for validation and physical insight. Rather than imposing existing models, we use them as reference frameworks to constrain and interpret the symbolic outputs. This data-driven yet physics-informed workflow reveals compact, generalizable laws for non-Newtonian behavior and opens new directions for predictive modeling of thixotropic and viscoplastic systems in flow assurance.
