Elastic versus viscoelastic physics-informed neural networks for transient flow modeling in high-density polyethylene pipes

Abstract

This paper highlights a crucial aspect of physics-informed neural networks (PINNs): their success hinges on accurately capturing the dominant physical mechanisms. This principle is illustrated for fluid-borne transient waves within high-density polyethylene (HDPE) pipelines by comparing two PINN formulations across negligible- and dominant-viscoelastic regimes. Utilizing numerical and experimental test rigs, an elastic PINN, based on the classical wave equation, was contrasted with a viscoelastic PINN incorporating a generalized Kelvin–Voigt representation of HDPE wall rheology. The analysis reveals a critical threshold dictated by the Deborah number (De=τ/Ts), which compares the HDPE pipe wall's viscoelastic retardation time (τ) with the excitation timescale (Ts) associated with the fluid-borne wave. In numerical simulations, viscoelastic retardation is negligible when De≫1, and both formulations achieve comparable accuracy with nearly identical convergence rates. For De∼O(1), the elastic PINN can partially compensate for the neglected viscoelastic effects through data-driven learning, but requires substantially more training iterations. Under these conditions, the viscoelastic PINN converges more than 50% faster while achieving comparable accuracy. In laboratory experiments under realistic noise and measurement uncertainty, the viscoelastic PINN achieves markedly higher accuracy than the elastic PINN, with correlation coefficients of 0.93 and 0.78, respectively, while converging an order of magnitude faster. These findings confirm that embedding the dominant physics improves the efficiency, consistency, and accuracy of PINN-based transient modeling.