Photometric Redshifts Probability Density Estimation from Recurrent Neural Networks in the DECam Local Volume Exploration Survey Data Release 2

Photometric wide-field surveys are imaging the sky in unprecedented detail. These surveys face a significant challenge in efficiently estimating galactic photometric redshifts while accurately quantifying associated uncertainties. In this work, we address this challenge by exploring the estimation of Probability Density Functions (PDFs) for the photometric redshifts of galaxies across a vast area of 17,000 square degrees, encompassing objects with a median 5$σ$ point-source depth of $g$ = 24.3, $r$ = 23.9, $i$ = 23.5, and $z$ = 22.8 mag. Our approach uses deep learning, specifically integrating a Recurrent Neural Network architecture with a Mixture Density Network, to leverage magnitudes and colors as input features for constructing photometric redshift PDFs across the whole DECam Local Volume Exploration (DELVE) survey sky footprint. Subsequently, we rigorously evaluate the reliability and robustness of our estimation methodology, gauging its performance against other well-established machine learning methods to ensure the quality of our redshift estimations. Our best results constrain photometric redshifts with the bias of $-0.0013$, a scatter of $0.0293$, and an outlier fraction of $5.1\%$. These point estimates are accompanied by well-calibrated PDFs evaluated using diagnostic tools such as Probability Integral Transform and Odds distribution. We also address the problem of the accessibility of PDFs in terms of disk space storage and the time demand required to generate their corresponding parameters. We present a novel Autoencoder model that reduces the size of PDF parameter arrays to one-sixth of their original length, significantly decreasing the time required for PDF generation to one-eighth of the time needed when generating PDFs directly from the magnitudes.