Physics-Informed Neural Networks for Steady Viscoelastic Flows in Fiber Spinning and Extrusion Film Casting

Abstract

We investigate Physics-Informed Neural Networks (PINNs) for two classical steady-state viscoelastic flow problems in polymer processing: fiber spinning and extrusion film casting. Both problems are governed by coupled nonlinear differential equations with viscoelastic constitutive behavior and serve as useful test cases for assessing PINNs on structured boundary-value problems. For the fiber-spinning model, we employ a modular PINN architecture with separate networks for area, velocity, and stress. For the extrusion film-casting model, we use a monolithic PINN that jointly predicts velocity, geometry, and stress fields while also inferring an unknown stress-related parameter. In both cases, the PINN solutions are validated against numerical reference solutions obtained from conventional integration-based methods. The results show that PINNs can recover the principal steady solution fields with high accuracy for the parameter regimes considered. For fiber spinning, the modular architecture yields strong agreement with the numerical solution across all variables. For extrusion film casting, the baseline PINN captures the kinematic variables well, while stress prediction is more challenging because of stiffness and steep gradients. This difficulty is substantially reduced by using adaptive activation functions, leading to marked improvement in stress-field accuracy. In addition, the unknown model parameter in the film-casting problem is inferred with good agreement relative to the numerical reference value. These results indicate that PINNs provide a flexible mesh-free framework for solving and parameterizing steady viscoelastic flow models, while also highlighting the greater difficulty of accurately resolving stress fields in stiff regimes.