Simulation of Steady Viscoelastic Creeping Flows with Physics-Informed Neural Networks

Viscoelastic fluid flows are governed by highly nonlinear, coupled mass, momentum, and constitutive equations, which pose significant challenges for numerical simulation. Although such flows have been extensively studied using conventional discretization-based methods, their simulation using physics-informed neural networks (PINNs) has received little attention. This work investigates PINNs as a mesh-free framework for simulating steady-state viscoelastic fluids under creeping flow conditions. Training is performed solely by minimizing the residuals of the governing partial differential equations and enforcing boundary conditions, without using reference solution data. The proposed approach is applied to the lid-driven cavity benchmark problem using the Oldroyd-B and the linear form of Phan-Thien-Tanner (PTT) constitutive models. For the Oldroyd-B model, accurate predictions of velocity, pressure, and polymeric extra-stress tensor fields are obtained without requiring tailored training strategies. For the PTT model, however, its strong nonlinearity with respect to the polymeric extra-stress tensor components makes appropriate initialization strategies essential for achieving accurate and robust predictions. Regardless of the constitutive model, at higher elasticity levels, the combination of a second-order optimization algorithm with double precision computations proved instrumental in achieving accurate predictions of the polymeric extra-stress tensor. Overall, the results presented in this work show the significant potential of PINNs as a viable methodology for modeling viscoelastic fluid flows.