MaRDIMark: the MaRDI benchmarking framework and its instances

Research software plays a pivotal role in the modern science workflows, yet numerical experiments often suffer from limitations in reliability, robustness, and interoperability. Despite the development of novel algorithms, their adoption across diverse domains is hindered by the challenges of integrating them into existing workflows. Furthermore, the absence of standardized benchmarks impedes the transparent and reproducible evaluation of algorithm performance. To address these challenges, we propose a standardized specification for benchmarking and evaluating algorithm performance across various mathematical domains. We demonstrate the implementation of MaRDIMark through specific instances tailored to model order reduction, gas network simulation and linear algebra applications. Designed with extensibility, customizability, and reproducibility in mind, these instances offer a flexible and domain-independent approach to benchmarking, facilitating broader adoption and comparative analysis within and across mathematical communities.