Bayesian deep learning for weak lensing analyses : overlapping galaxies separation and galaxy parameters estimation from blended scenes

Weak gravitational lensing is one of the most promising probes to constrain dark energy parameters. It corresponds to the distortion of a source image, induced by the bending of space-time, thus of the light path, generated by the presence of mass along the line of sight. This effect is small and can only be detected measuring the correlation of the shapes of a group of background galaxies. The value of this correlation yields the value of the cosmic shear. Several surveys dedicated to its study are going to start soon, such as the Vera Rubin Legacy Surveys of Space and Time (LSST), and Euclid. These surveys have been built with particular requirements, especially about the treatment of systematic errors, in order to reach an extreme precision on the dark energy equation of state parameters. This thesis happened in the context of the Dark Energy Science Collaboration (DESC), inside the LSST experiment. It focuses on the issue of blending, the overlap of astronomical sources. The blending of galaxies introduces a dominant systematic uncertainty on the cosmic shear measurement. This systematic effect impacts the shape and the redshift measurements, both necessary for weak gravitational lensing analysis. We propose two avenues based on Bayesian deep learning methods. The first one is a deblending algorithm which uses a deep generative network called variational autoencoder. This neural network allows to learn a prior for the generation of isolated galaxy images. The latter is used in a second network to perform the deblending of the centred galaxy on images of simulated galaxies. We show that the pixel joint analysis of LSST and Euclid data decreases the median error on galaxy shape reconstruction from 8 to 47%. Blending of sources being closely linked to detection, we demonstrate that our method is robust to small decentring. Also we test our method on images of real galaxies artificially blended showing the interest of transfer learning from a neural network trained on simulated galaxy images. An iterative process is then designed in order to separate all the galaxies in an image going through detection, classification and deblending of sources. Finally this deblending algorithm is tested on images extracted from the DC2 simulation, generated within the DESC to prepare for the analysis of futures images taken by LSST. Our results show an improvement of 70 to 120% on the median error on galaxy shape reconstruction compared to the generic method used in the current LSST pipeline. Then, inspired by this first method, we propose a neural network allowing for the direct estimation of galaxy shape and redshift parameters from DC2 images, without going through the deblending. We show that this neural network allows for a precise measurement of these parameters, even when sources are blended, and we compare these results to the ones obtained with deblending. Then we present the first application of a Bayesian neural network to galaxy shapes estimation. This kind of network provides the estimation of the epistemic uncertainty which characterizes the uncertainty coming from the training sample. It can be viewed as a confidence level in the measurement performed by the network, a primordial information for the application of neural networks in science and in cosmology. It can be used to decrease the importance (or reject) of an incorrect measurement in the analysis. (author)