MITIGATING SHOCK PHENOMENON OF HYPERBOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH PHYSICS INFORMED NEURAL NETWORKS

Abstract

Understanding viscoelastic flows and their conservational laws is crucial for various applications, often described by hyperbolic partial differential equations (PDEs) that can present challenges in numerical simulations due to shock behaviours. Introducing artificial viscosity is essential to mitigate shocks, with significant impact on simulation accuracy. This thesis explores the application of Physics-informed Neural Networks (PINNs) to address adaptive artificial viscosity, focusing on inviscid Burgers equations in 1D and 2D cases. Three approaches are discussed, aiming to improve understanding and offer innovative tools for enhancing numerical simulation accuracy in viscoelastic flows.