A Staged Physics-Informed Neural Network Framework for Viscoelastic Stress Prediction and Pressure Recovery in Polymer Melt Flow

Abstract

Abstract

Polymer melt flows are typically accompanied by pronounced viscoelastic effects. Accurate acquisition of the stress and pressure fields during the flow process is of great significance for revealing their transient evolution mechanisms and analyzing related processing behaviors. Although traditional numerical methods can solve the governing equations of viscoelastic flows, they still suffer from high computational cost and implementation complexity in stress computation, pressure recovery, and the characterization of temporal memory effects. In this paper, a low-Reynolds-number two-dimensional Poiseuille-type polymer melt channel flow is considered, and a staged physics-informed neural network framework is developed for viscoelastic stress prediction and pressure field recovery. In the integer-order case, the discrete velocity data are first organized onto a spatio-temporal grid, and then the spatio-temporal coordinates are taken as inputs to predict the three stress components. Based on the predicted stress field, the pressure field is further recovered through the momentum equations, thereby forming a staged solution strategy of “stress prediction-pressure recovery.” After verifying the feasibility of the integer-order model, a time-fractional derivative is introduced, and the historical memory effect in polymer melt flow is characterized by the fractional order α. Meanwhile, the influence of different fractional orders on the stress evolution process is analyzed. The experimental results show that the integer-order model can effectively predict the overall distribution characteristics of the viscoelastic stress components and the pressure field, and the recovered pressure preserves the basic linear decay pattern along the flow direction. In the fractional-order model, while the main spatial structure of the stress field remains stable, the response intensity of the stress components can be regulated by α, which reflects the influence of temporal memory effects on the stress evolution process.