Many problems in computational mechanics involve the solution of large, sparse linear systems, either as an intrinsic step of the numerical algorithm or as the result of linearization. Solving these systems is often computationally intensive and constitutes a major performance bottleneck, making it a natural target for optimization. While a wide variety of solution methods exist, iterative methods are preferred, as direct methods often exceed the available system memory [1]. However, iterative methods can vary significantly in effectiveness depending on the problem at hand. While some methods may be able to solve a broader range of problems, others may be faster when convergent. Existing strategies often rely on expensive features, lack robustness across problems, or fail to balance performance with scalability. Our work investigates whether learned embeddings can substitute the computation (or estimation) of informative but expensive matrix features (e.g., condition number estimates or other spectral information) while maintaining reliable solver selection across diverse sparse systems. Building on the performance modeling approaches of Yeom et al. [2] and Tang et al. [3], we propose a learning-based solver ranking framework that achieves this by using low-cost learned embeddings (Fig. 1). The framework supports flexible embedding strategies and incorporates more comprehensive performance metrics (such as Absolute Relative Error, or ARE) to better assess solver quality and reliability. The proposed scheme improves solver ranking accuracy and stability relative to classical methods, default choices, and single-best strategies, while reducing variance across problem instances (Tab. 1). Overall, the proposed framework provides a data-driven yet lightweight improvement over classical solver selection strategies, making it well-suited for large-scale computational mechanics workflows. References: [1] Saad, Yousef. Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics, 2003. [2] Yeom, Jae-Seung, et al. Data-driven performance modeling of linear solvers for sparse matrices. 7th International Workshop on Performance Modeling, Benchmarking and Simulation of High Performance Computer Systems (PMBS). IEEE, 2016. [3] Tang, Ziyuan, et al. Graph neural networks for selection of preconditioners and Krylov solvers. NeurIPS 2022 Workshop: New Frontiers in Graph Learning. 2022.