Embedding-Based Methods for the Selection of Iterative Linear Solvers and Preconditioners

The solution of sparse linear systems is central to many large-scale scientific computing problems, where the choice of solver and preconditioner strongly correlates with overall execution time and solution quality. However, an ever-expanding number of implementations available across distinct numerical libraries makes choosing the most efficient combination (or sometimes even a stable and convergent one) for a given problem challenging, particularly for non-expert users. This work presents a novel pipeline leveraging embedding and linear modelling techniques and compares it to classic machine learning approaches to the solver-preconditioner selection problem. We then apply the developed model to a selection of Krylov solver implementations and preconditioners from the PETSc framework over different datasets. We then use different metrics to analyze the results, since the raw accuracy value can be misleading, given the imbalance in the data. Beyond raw accuracy, we analyze multiple performance metrics, since imbalanced datasets often render standard accuracy misleading. Results demonstrate that embedding-based selection achieves better ranking-based and error-based scores, with competitive performance even when trained with only cheap features, compared to the classic black-box approaches using all features, highlighting the method's robustness and applicability and scalability in parallel solver selection tasks.     «

The solution of sparse linear systems is central to many large-scale scientific computing problems, where the choice of solver and preconditioner strongly correlates with overall execution time and solution quality. However, an ever-expanding number of implementations available across distinct numerical libraries makes choosing the most efficient combination (or sometimes even a stable and convergent one) for a given problem challenging, particularly for non-expert users. This work presents a...     »