High Order Solver

High-order solvers are numerical methods designed to efficiently and accurately solve complex mathematical problems, particularly differential equations, by employing higher-degree polynomial approximations. Current research emphasizes automating solver parameters and adaptation strategies, often using reinforcement learning to optimize mesh refinement (h/p-adaptation), multigrid methods, and even the choice of solver itself depending on problem characteristics. This focus on automation improves computational efficiency and robustness, leading to faster simulations and more reliable results across diverse applications, including fluid dynamics, stochastic differential equations, and machine learning. The resulting advancements have significant implications for various scientific fields and engineering applications requiring high-fidelity simulations.