The field of numerical methods for complex systems is rapidly advancing, with a focus on developing efficient and accurate algorithms for solving high-dimensional nonlinear problems. Recent developments have centered around the creation of innovative numerical schemes, such as parallelized computation methods, iterative linearized solvers, and adaptive splitting schemes, which enable the solution of complex systems with increased speed and accuracy. Notably, the integration of machine learning techniques, such as automatic differentiation, is being explored to enhance the efficiency and robustness of numerical methods. Furthermore, researchers are investigating the application of novel numerical approaches, including generalized plane wave quasi-Trefftz spaces and radial basis function finite difference methods, to tackle challenging problems in wave propagation and dispersive wave equations. Overall, these advancements have the potential to significantly impact various fields, including engineering, physics, and computer science, by enabling the simulation and analysis of complex systems with unprecedented accuracy and efficiency.

Noteworthy papers include: The paper on the Harmonic Balance-Automatic Differentiation method, which proposes an efficient solver for general nonlinear dynamics simulation by integrating automatic differentiation with the harmonic balance framework. The paper on the Random Greedy Fast Block Kaczmarz method, which presents a novel approach for solving large-scale nonlinear systems by combining random and greedy strategies.