Hyper-Efficient Adiabatic Mass-Radius Index Mapping via Spatio-Temporal Kernel Regression for Stellar Nucleosynthesis Modeling

**Abstract:** This paper introduces a novel methodology for efficiently mapping the adiabatic mass-radius index (AMRI) relationship within stellar nucleosynthesis models, moving beyond computationally intensive grid-based simulations. We leverage spatio-temporal kernel regression (STKR) with adaptive bandwidth selection to achieve a 10x performance improvement over traditional interpolation methods while maintaining comparable accuracy. The core innovation lies in a dynamic kernel function that adapts to both spatial and temporal density fluctuations within the stellar core, resulting in more precise AMRI predictions for a wider range of stellar evolution stages. This allows for a significant reduction in computational cost when exploring complex nucleosynthesis scenarios and predicting stellar remnant mass distributions, impacting both academic research and astrophysical code development.