Numerical Discretization

Numerical discretization, the process of approximating continuous mathematical problems with discrete representations suitable for computation, is crucial across scientific and engineering disciplines. Current research emphasizes developing more efficient and accurate discretization methods, particularly focusing on integrating machine learning techniques (e.g., neural networks, neural operators) with established numerical methods (e.g., finite element, finite volume, finite difference) to improve accuracy, reduce computational cost, and handle complex geometries or irregular domains. These advancements are significantly impacting fields like fluid dynamics, structural mechanics, and image processing by enabling faster and more robust simulations and analyses.