The field of numerical methods for complex systems is witnessing significant advancements, driven by the need for efficient and accurate simulations of various phenomena. A key direction in this field is the development of innovative algorithms and techniques that can effectively capture the behavior of complex systems, such as those involving multiple scales, high dimensions, and nonlinear interactions. Notably, researchers are exploring the use of tensor-based methods, hierarchical approaches, and adaptive refinement strategies to improve the accuracy and efficiency of simulations. These advancements have the potential to impact a wide range of applications, from materials science and biology to fluid dynamics and electromagnetism.

Some noteworthy papers in this regard include: The paper on Matrix- and tensor-oriented numerical schemes for the evolutionary space-fractional complex Ginzburg--Landau equation, which proposes efficient methods for solving complex equations. The paper on MultiLevel Variational MultiScale framework for large-scale simulation, which introduces a novel approach for seamless integration of multilevel mesh strategies into the Variational Multiscale framework. The paper on A Semi-Lagrangian Adaptive Rank Method for High-Dimensional Vlasov Dynamics, which extends a semi-Lagrangian adaptive rank integrator to the general high-order tensor setting, enabling the simulation of Vlasov models in up to six dimensions.