The field of numerical methods for complex systems is rapidly evolving, with a focus on developing innovative and efficient algorithms for solving partial differential equations, simulating complex phenomena, and analyzing large datasets. Recent research has led to significant advancements in areas such as finite element methods, multigrid techniques, and stochastic simulations. Notably, the development of new numerical schemes, such as the multigrid method for CutFEM and the kernel compression method for distributed-order fractional partial differential equations, has improved the accuracy and efficiency of simulations. Additionally, the application of machine learning techniques and high-performance computing has enabled the solution of complex problems in fields such as materials science, fluid dynamics, and biology. Some noteworthy papers in this area include the work on a finite element framework for simulating residential burglary, which demonstrates the potential of numerical methods for modeling complex social phenomena, and the development of a cubed sphere fast multipole method, which enables efficient simulations of particle interactions on the sphere. Overall, the field is moving towards the development of more sophisticated and specialized numerical methods, with a focus on addressing specific challenges and applications.