Leveraging Deep Learning for Time Series Extrinsic Regression in predicting photometric metallicity of Fundamental-mode RR Lyrae Stars

Astronomy is entering an unprecedented era of Big Data science, driven by missions like the ESA's Gaia telescope, which aims to map the Milky Way in three dimensions. Gaia's vast dataset presents a monumental challenge for traditional analysis methods. The sheer scale of this data exceeds the capabilities of manual exploration, necessitating the utilization of advanced computational techniques. In response to this challenge, we developed a novel approach leveraging deep learning to estimate the metallicity of fundamental mode (ab-type) RR Lyrae stars from their light curves in the Gaia optical G-band. Our study explores applying deep learning techniques, particularly advanced neural network architectures, in predicting photometric metallicity from time-series data. Our deep learning models demonstrated notable predictive performance, with a low mean absolute error (MAE) of 0.0565, the root mean square error (RMSE) achieved is 0.0765 and a high $R^2$ regression performance of 0.9401 measured by cross-validation. The weighted mean absolute error (wMAE) is 0.0563, while the weighted root mean square error (wRMSE) is 0.0763. These results showcase the effectiveness of our approach in accurately estimating metallicity values. Our work underscores the importance of deep learning in astronomical research, particularly with large datasets from missions like Gaia. By harnessing the power of deep learning methods, we can provide precision in analyzing vast datasets, contributing to more precise and comprehensive insights into complex astronomical phenomena.