The field of numerical methods for complex systems is moving towards the development of innovative and efficient algorithms for solving high-dimensional problems. Researchers are focusing on creating mesh-free, derivative-free, and matrix-free methods that can be parallelized and are suitable for solving ultra-high-dimensional PDEs. Another area of interest is the development of bound-preserving schemes for Temple-class systems, which is crucial for avoiding non-physical solutions and ensuring robustness in simulations. Higher-order boundary conditions for atomistic dislocation simulations are also being explored, which can improve the accuracy and efficiency of simulations. Noteworthy papers in this area include:

• A mesh-free, derivative-free, matrix-free, and highly parallel localized stochastic method for high-dimensional semilinear parabolic PDEs, which provides explicit pointwise evaluations and is naturally suited for parallelization.
• A novel bound-preserving and conservative numerical scheme for non-convex sets in Temple-class systems, which introduces a moving mesh approach and a parameterized flux limiter to restrict high-order fluxes.
• A higher-order boundary condition for atomistic simulations of dislocations, which combines continuum predictor solutions with discrete moment corrections to enable systematically improvable high-order boundary conditions.