Linear System

Linear systems, representing a fundamental mathematical framework for modeling diverse phenomena, are central to numerous scientific and engineering disciplines. Current research focuses on efficiently solving large-scale linear systems, often employing iterative methods like GMRES preconditioned by machine learning models such as graph neural networks or learned incomplete factorizations. These advancements aim to improve the speed and robustness of solving linear systems arising from applications such as partial differential equations and control systems, impacting fields ranging from structural engineering to machine learning. The development of novel algorithms and the application of machine learning techniques are driving significant progress in this area.