Le Département d'Électronique des Détecteurs et d'Informatique pour la Physique

The upcoming stage-IV Dark Energy surveys, such as Euclid and LSST, will observe the
Universe with unprecedented accuracy, allowing us to investigate fundamental problems in
cosmology. These surveys will use weak gravitational lensing as one of the main probes to
investigate the origin of the accelerated expansion of the Universe and the properties of
its dark matter component. 

However, traditional cosmological inference for weak gravitational lensing has two
important limitations: First, the two-point statistics do not fully extract the
non-Gaussian information from cosmological data. Second, even for the two-point
statistics, writing down an accurate model for the likelihood function can be very arduous
(small-scale uncertainties, non-Gaussian signals, etc.). 

In recent years, it has been shown that statistics of order higher than a second can help
to access non-Gaussian information, nevertheless, these approaches are characterized by
the absence of analytical models to describe the observed signal and require calibrating
the cosmology inference from weak lensing simulations. 

One possible way to circumvent an explicit likelihood consists in using Likelihood-free
inference methods. These methods estimate posterior distributions through forward modeling
of simulated data. Alternatively, Bayesian forward-modeling methods can be used, which
integrate observations into a forward model, enabling the exact reconstruction of the
likelihood.

All the methodologies and developments in this thesis work towards two major goals: making
fast approximated simulations suitable for the data analysis pipeline of upcoming
cosmological surveys and investigating forward modeling techniques to exploit the
potential of next-generation weak lensing data. \

In this context, we have developed and validated the Differentiable Lensing Lightcone
(DLL) package within the LSST framework. DLL is a fully automatically differentiable
physical model designed for fast inference, aiming to achieve high accuracy with low
computational costs.  The DLL tool is designed to be used as a forward model in Bayesian
inference algorithms requiring access to the derivatives of the likelihood of the model. 

We have also developed a new correction scheme to enhance the accuracy of quasi-N-body
simulations, aiming to replicate the precision of high-resolution N-body simulations.

Finally, we investigate the performance of different procedures to optimally extract
informative summaries obtained from mock weak lensing mass maps compressed using
Convolution Neural Networks.

-          Keywords:  

Weak gravitational lensing; cosmology; higher order statistics;  cosmological simulations;
Dark energy; automatic differentiation;

-          Thesis supervisor: Jean-Luc Starck

-          Jury members : Jean-Luc Starck, Alan Heavens,  Roberto Trotta, Anne Ealet ,
Vincenzo Fabrizio, François Lanusse