Differential Operator

Differential operators are mathematical objects that map functions to other functions, often representing rates of change or transformations. Current research focuses on efficiently applying these operators within various computational frameworks, including physics-informed neural networks (PINNs) and neural operators, to solve partial differential equations (PDEs) and improve data generation for machine learning models. This work addresses challenges like ill-conditioning in training PINNs and developing more accurate and efficient methods for approximating differential operators, particularly in high-dimensional spaces and on complex geometries. These advancements have significant implications for scientific computing, enabling faster and more accurate simulations across diverse fields, from fluid dynamics to material science.