High Order

High-order methods aim to improve the efficiency and accuracy of various computational tasks by leveraging higher-order derivatives or approximations. Current research focuses on applying these methods to diverse areas, including machine learning (e.g., developing more efficient and complete molecular property prediction models), numerical solutions of differential equations (e.g., accelerating diffusion models in image generation and improving solvers for fluid dynamics), and optimization algorithms (e.g., achieving optimal convergence rates in convex optimization and variational inequalities). These advancements offer significant potential for accelerating computations, enhancing model accuracy, and improving the efficiency of various scientific and engineering applications.