Numerical Solution

Numerical solutions for partial differential equations (PDEs) are crucial across scientific and engineering disciplines, but their computational cost and complexity drive the search for efficient alternatives. Current research focuses on machine learning approaches, particularly physics-informed neural networks (PINNs) and methods incorporating large language models (LLMs) to leverage both data and known system information for improved accuracy and efficiency. These advancements are impacting diverse fields, from fluid dynamics simulations and robotics to online machine learning and scientific super-resolution, by providing faster and more accurate solutions to complex problems.