ViscoelasticNet: A physics informed neural network framework for stress discovery and model selection

Abstract

Viscoelastic fluids are a class of fluids that exhibit both viscous and elastic nature. Modelling such fluids requires constitutive equations for the stress, and choosing the most appropriate constitutive relationship can be difficult. We present viscoelasticNet, a physics-informed deep learning framework that uses the velocity flow field to select the constitutive model and learn the stress field. Our framework requires data only for the velocity field, initial \& boundary conditions for the stress tensor, and the boundary condition for the pressure field. Using this information, we learn the model parameters, the pressure field, and the stress tensor. {This work considers} three commonly used non-linear viscoelastic models: Oldroyd-B, Giesekus, and linear Phan-Thien-Tanner (PTT). We demonstrate that our framework works well with noisy and sparse data. Our framework can be combined with velocity fields acquired from experimental techniques like particle image velocimetry to get the pressure \& stress fields and model parameters for the constitutive equation. Once the model has been discovered using viscoelasticNet, the fluid can be simulated and modeled for further applications.