Burger Equation

The Burgers equation, a fundamental nonlinear partial differential equation, serves as a crucial testbed for modeling diverse phenomena, from fluid dynamics to cosmology. Current research focuses on efficiently solving the equation using advanced numerical methods, particularly Physics-Informed Neural Networks (PINNs) and variations incorporating techniques like implicit Euler transfer learning and multi-grade deep learning architectures to improve accuracy and reduce computational cost. These advancements are improving the ability to model complex systems accurately and efficiently, impacting fields ranging from computational fluid dynamics to petroleum engineering.