Predicting sparse linear systems partition number using machinelearning

This thesis proposes a machine learning approach to solve sparse linear systems, a common problem in science and engineering. Our method uses machine learning to predict the optimal number of partitions needed for the block cimmino method. Traditional methods typically rely on trial and error or choosing the maximum number of cores as partitions to determine the best number of blocks. However, using a trained machine learning model eliminates this process. In this work, we present two models: one predicts two partition numbers with an AUC score of 89%, and the other predicts multiple partition numbers with an AUC score of 76% for the block cimmino method. We achieve this by using previously identified features in the literature and applying them in a novel context. We trained and tested our models using a diverse set of matrices, incorporating feature selection, demonstrating the effectiveness of leveraging established features in new applications and the robustness of our model in addressing the challenges of partitioning sparse linear systems. Our proposed method is faster and more effective than traditional methods.