Deep Probabilistic Modeling of Weak Lensing Mass Maps

While weak gravitational lensing is one of the most promising cosmological probes targeted by upcoming wide-field surveys, exploiting the full information content of the cosmic shear signal remains a major challenge. One dimension of this challenge is the fact that analytic cosmological models only describe the 2pt functions of the lensing signal, while we know the convergence field to be significantly non-Gaussian. As a result, solving a problem like weak lensing mass-mapping using analytic Gaussian priors will be sub-optimal. We do however have access to models that can capture the full statistics of the lensing signal: numerical simulations. But the question is: how can we use samples from numerical simulations to solve a Bayesian inference problem such as weak lensing mass-mapping?

In this talk, I will illustrate how recent deep generative modeling provides us with the tools needed to leverage a physical model in the form of numerical simulations to perform proper Bayesian inference.

Using Neural Score Estimation, we learn from numerical simulations an estimate of the score function (i.e. the gradient of the log density function) of the distribution of convergence maps. We then use the learned score function as a prior within an Annealed Hamiltonian Monte-Carlo sampling scheme which allows us to access the full posterior distribution of a mass-mapping problem, in 10⁶ dimensions.