Simulation-based inference benchmark for weak lensing cosmology

Context. Standard cosmological analysis, which is based on two-point statistics, fails to extract all the information embedded in the cosmological data. This limits our ability to precisely constrain cosmological parameters. Through willingness to use modern analysis techniques to match the power of upcoming telescopes, recent years have seen a paradigm shift from analytical likelihood-based to simulation-based inference. However, such methods require a large number of costly simulations. Aims. We focused on full-field inference, which is considered the optimal form of inference as it enables the recovery of cosmological constraints from simulations without any loss of cosmological information. Our objective is to review and benchmark several ways of conducting full-field inference to gain insight into the number of simulations required for each method. Specifically, we made a distinction between explicit inference methods that require an explicit form of the likelihood, such that it can be evaluated and thus sampled through sampling schemes and implicit inference methods that can be used when only an implicit version of the likelihood is available through simulations. Moreover, it is crucial for explicit full-field inference to use a differentiable forward model. Similarly, we aim to discuss the advantages of having differentiable forward models for implicit full-field inference. Methods. We used the sbi_lens package (https://github.com/DifferentiableUniverseInitiative/sbi_lens), which provides a fast and differentiable log-normal forward model to generate convergence maps mimicking a simplified version of LSST Y10 quality. While the analyses use a simplified forward model, the goal is to illustrate key methodologies and their implications. Specifically, this fast-forward model enables us to compare explicit and implicit full-field inference with and without gradient. The former is achieved by sampling the forward model through the No U-Turns (NUTS) sampler. The latter starts by compressing the data into sufficient statistics and uses the neural likelihood estimation (NLE) algorithm and the one augmented with gradient (δ NLE) to learn the likelihood distribution and then sample the posterior distribution. Results. We performed a full-field analysis on LSST Y10-like weak-lensing-simulated log-normal convergence maps, where we constrain (Ωc,Ωb,σ8,h0,ns,w0). We demonstrate that explicit full-field and implicit full-field inference yield consistent constraints. Explicit full-field inference requires 630 000 simulations with our particular sampler, which corresponds to 400 independent samples. Implicit full-field inference requires a maximum of 101 000 simulations split into 100 000 simulations to build neural-based sufficient statistics (this number of simulations is not fine-tuned) and 1000 simulations to perform inference using implicit inference. Additionally, while differentiability is very useful for explicit full-field inference, we show that, for this specific case, our way of exploiting the gradients does not help implicit full-field inference significantly.