The field of linear system solvers and optimization techniques is witnessing significant advancements, driven by the development of innovative methods and algorithms. Researchers are focusing on improving the efficiency and scalability of solvers for large-scale linear systems, which is crucial for various applications in science and engineering. Notably, the integration of artificial intelligence and machine learning techniques is leading to breakthroughs in areas such as adaptive search optimization and preconditioning. These advancements have the potential to accelerate the solution of complex problems and enable the simulation of large-scale systems.

Some noteworthy papers in this area include: HyP-ASO, which proposes a hybrid policy-based adaptive search optimization framework that combines a customized formula with deep Reinforcement Learning to solve large-scale Integer Linear Programs. Fast Linear Solvers via AI-Tuned Markov Chain Monte Carlo-based Matrix Inversion, which presents an AI-driven framework for recommending MCMC parameters to generate effective preconditioners for large, sparse linear systems. RGDBEK, which introduces a novel Kaczmarz approach designed for efficient large-scale linear system solutions, employing a randomized selection strategy to mitigate the traditional seesaw effect and enhance convergence robustness. Preconditioning via Randomized Range Deflation (RandRAND), which introduces a new class of randomized preconditioning methods that deflate the spectrum via efficient orthogonal projections onto random subspaces, leading to advantages in computational cost and numerical stability.