Beijing Institute of Mathematical Sciences and Applications

Solving large sparse linear systems is the main computational bottleneck in multiphysics simulation. Traditional iterative solvers face a fundamental trilemma, struggling to combine efficiency, robustness, and usability. This talk presents a novel framework that breaks this deadlock by merging multilevel solvers with data-driven learning. We will outline our preliminary steps to break the trilemma, including the optimization of multilevel components and new preconditioners for coupled PDE systems. By automating solver parameter tuning within a modular software architecture, our work tries to pave the way for intelligent, adaptive, and scalable solver technology for next-generation scientific simulations.