(522c) Non-Newtonian Neural Network, N4, a Machine Learning Framework for Solving Non-Newtonian Fluid Problems

Non-Newtonian fluids exhibit various responses based on their internal structure; hence, accurate flow behavior prediction of these fluids is of great interest across many disciplines in industrial and academic settings alike. The challenge is to solve the coupled Partial Differential Equations (PDEs) consisting of equation motion of the fluid and the stress formulations to fully capture the behavior of these structured fluids under various flow protocols, and for different complex geometries and boundary conditions. We present Non-Newtonian Neural Network (N⁴) for solving systems of coupled PDEs adopted for complex fluids. The proposed N⁴ algorithms are employed to solve the constitutive models in copulation with conservation of momentum by benefiting from Automatic Differentiation (AD) in neural networks. This method is tested for various complex fluids with different constitutive models in several flow protocols. These include a range of Generalized Newtonian Fluids (GNF) empirical constitutive models, as well as some phenomenological models with embedded material timescales (memory effects). The proposed N⁴ platform is found to recover the full solution of a complex fluid in a spatiotemporal domain with excellent accuracy compared to the ground truth solution.