Nonlocal Operator

Nonlocal operators are mathematical tools that model interactions extending beyond immediate neighbors, unlike local operators. Current research focuses on improving their efficiency and accuracy in diverse applications, including machine learning (where they address computationally expensive "NonGEMM" operations), image processing (e.g., multi-view stereo reconstruction using epipolar geometry constraints), and solving complex partial differential equations (like fractional Fokker-Planck equations). This involves developing novel algorithms, such as Monte Carlo methods and adaptive deep learning approaches, and addressing challenges like kernel learning and high-dimensional problems. The improved understanding and application of nonlocal operators promise advancements in various fields, from accelerating machine learning models to enabling more accurate simulations of physical phenomena.