Artificial Neural Networks Solutions for Solving Differential Equations: A Focus and Example for Flow of Viscoelastic Fluid with Microrotation

Abstract

Physics-informed neural networks (PINN) are an artificial neural network (ANN) approach for solving differential equations. PINN offers an alternative to classical numerical methods. The paper discusses the applications of PINN in various domains by highlighting the advantages, challenges, limitations, and some future directions. For example, PINN is implemented to solve the differential equations describing the Flow of Viscoelastic Fluid with Microrotation at a Horizontal Circular Cylinder Boundary Layer. The differential equations resulting from a nondimensionalization process of the governing equations and the associated boundary conditions are solved using PINN. The obtained results using PINN are discussed and compared to other state-of-the-art methods. Future research might aim to increase the precision and effectiveness of PINN models for solving differential equations, either by adding more physics-based restrictions or multi-scale methods to expand their capabilities. Additionally, investigating new application domains like linked multi-physics issues or real-time simulation situations may help to increase the reach and significance of PINN approaches.