Data-Driven Solver Selection for Sparse Linear Matrices at Scale

Sparse linear systems sit at the core of many computational problems, and their solution strongly correlates to overall execution time. However, with the constant increase of the number of linear solver and preconditioner implementations available across a plethora of numerical libraries, choosing the most efficient combination for a given problem (in terms of time-to-solution) is a challenging task. Indeed, even selecting a numerically stable combination may seem to be an unsurmountable endeavor, especially for a novice user. This is particularly evident when observing performance at scale, where the HPC system architecture and even the number of cores used can make a drastic difference. In this work, we compare previous machine learning approaches to the solver-preconditioner selection problem and develop a performance model for a selection of Krylov solver implementations and preconditioners in the PETSc framework over the SuiteSparse matrix collection. We then use the developed model to address the selection of an optimal solver for a given input matrix, showing that the current approach performs better than the black-box approach on a broad range of systems.     «

Sparse linear systems sit at the core of many computational problems, and their solution strongly correlates to overall execution time. However, with the constant increase of the number of linear solver and preconditioner implementations available across a plethora of numerical libraries, choosing the most efficient combination for a given problem (in terms of time-to-solution) is a challenging task. Indeed, even selecting a numerically stable combination may seem to be an unsurmountable endeavo...     »