Hyperbolic Partial Differential Equation

Hyperbolic partial differential equations (PDEs), characterized by wave-like propagation and potential discontinuities, pose significant challenges for numerical solution. Current research focuses on developing robust and efficient deep learning methods, including physics-informed neural networks (PINNs) and their variants (e.g., RelaxNN, wPINNs), and operator learning approaches like Fourier Neural Operators, to accurately capture solutions, particularly those involving shocks. These advancements aim to overcome limitations of traditional numerical techniques in handling discontinuities and offer faster, more scalable solutions for diverse applications, such as fluid dynamics and traffic flow modeling.