Selecting the right solver and preconditioner for large sparse linear systems Ax=b is critical for computational efficiency across many scientific and engineering fields. This process requires significant domain expertise or costly benchmarking. MM-AutoSolver demonstrated that a multimodal CNN+MLP architecture combining a sparsity-pattern image with matrix features can automate this selection. This thesis extends that approach by systematically evaluating 14 image encoding strategies at different resolutions, introducing dual-channel CNN inputs that use pairs of image encodings in parallel, a convergence penalty to reduce solver failure rates, and an ensemble of independently trained models. The key finding is that magnitude-based image encodings consistently outperform other encoding methods. Combining it with a complementary image mode in the dual-channel CNN input increases F1 by 2.2% over the best single-channel approach. An ensemble of four dual-channel models achieves a 66.77% macro F1, surpassing the MM-AutoSolver approach by approximately 4% in F1 despite operating on a harder and more class-balanced dataset.     «

Selecting the right solver and preconditioner for large sparse linear systems Ax=b is critical for computational efficiency across many scientific and engineering fields. This process requires significant domain expertise or costly benchmarking. MM-AutoSolver demonstrated that a multimodal CNN+MLP architecture combining a sparsity-pattern image with matrix features can automate this selection. This thesis extends that approach by systematically evaluating 14 image encoding strategies at differe...     »