Neural Linear Solvers and Preconditioners for General Sparse Matrices

Adapting applications to take full advantage of exascale supercomputers, including accelerators such as GPUs, is a major challenge, requiring significant changes to application codes.
Numerical simulation is a strategic tool for many IFPEN applications requiring the modeling of multiphase flows. The performance of these simulators is therefore a major concern. In particular, it has a direct impact on the quality of results and the ability to perform large-scale calculations. In many of IFPEN's numerical simulators, solving linear systems, which are often ill-conditioned, is the most time-consuming step.
In this context and during the PhD thesis, several aspects will be addressed both on the study of the numerical convergence of the preconditioned linear system resolution thanks to Artificial Intelligence (AI) and also on the possibility of using the trained networks with a performance guarantee in the complete applications where the conditioning of the matrix changes during time steps. Indeed, current advances in this field, both on the numerical and computational domains, motivate us to investigate further in this direction.Hybrid developed approaches will be evaluated in terms of CPU time and number of matrix-vector products required for convergence on representative test-cases arising from both IFPEN and ONERA typical applications.