The Shear-to-Cosmology Paradigm I: Hybrid Field-Level and Simulation-Based Framework for Weak Lensing Surveys

TL;DR

This work tackles the challenge of extracting non-Gaussian information from weak-lensing data by proposing a hybrid shear-to-cosmology framework that combines field-level inference (FLI) with simulation-based inference (SBI). A Transformer-based FLI network processes shear fields to produce informative feature representations, which SBI then maps to tight cosmological posteriors, using either ML-derived features or traditional 2PCFs as summaries. A blind PCA-based denoising scheme along the redshift axis preserves non-Gaussian information, and results show that shear-based inference nearly doubles constraining power over KS convergence, with gains up to 36.4% when combining PCA denoising and ML-derived features. The framework demonstrates a scalable, robust pathway to exploit the full information content of Stage-IV weak-lensing surveys, enabling more precise constraints on parameters such as $\Omega_m$ and $\sigma_8$.

Abstract

Precise cosmological inference from next-generation weak lensing surveys requires extracting non-Gaussian information beyond standard two-point statistics. We present a hybrid machine-learning (ML) framework that integrates field-level inference (FLI) with simulation-based inference (SBI) to map observed shear fields directly to cosmological parameters, eliminating the need for convergence reconstruction. The FLI network extracts rich non-Gaussian information from the shear field to produce informative features, which are then used by SBI to model the resulting complex posteriors. To mitigate noise from intrinsic galaxy shapes, we develop a blind, training-free, PCA-based shear denoising method. Tests on CSST-like mock catalogs reveal significant performance gains. The shear-based inference achieves approximately twice the cosmological constraining power in Figure of Merit (FoM) compared to the conventional convergence-based approach. Moreover, the combination of PCA denoising and ML compression can deliver a 36.4% improvement in FoM over standard shear two-point statistics. This work establishes a scalable and robust pathway for cosmological inference, unlocking the full potential of Stage-IV weak-lensing surveys.

Figures (11)

• Figure 1: Schematic overview of the proposed framework, consisting of: 1. a field-level inference (FLI) network (inside the dashed box) and 2. a simulation-based inference (SBI) module (outside the dashed box). The field-level shear input is a six-dimensional tensor with shape $(B,\,N_{\gamma},\,N_{z},\,N_{\rm blk},\,H,\,W)$$=$$(B,\,2,\,16,\,4,\,64,\,64)$, where $B$ is the batch size, $N_{\gamma}$ the shear components, $N_{z}$ the number of photo-$z$ slices, $N_{\rm blk}$ the number of blocks in each sky group (see Figure \ref{['fig: sky-108-block dataset']}), and $(H,W)$ the spatial map size. The FLI network comprises four components: (a) a redshift-direction embedding layer, (b) a $\gamma_1$ & $\gamma_2$ merging layer, (c) Transformer ($\mathtt{TransF}$)-based encoders, and (d) fully connected inference layers to predict $(\Omega_m,\,\sigma_8)$. In parallel, SBI is applied either to the ML-derived feature representation (red dashed box) or to conventional two-point statistics (2PCF). The same structure of FLI network is applied to convergence map $(\kappa)$ by duplicating it to form a two-component input $(\kappa,\,\kappa)$.
• Figure 2: Preparation of an input sky block for training the FLI network. At a resolution of $0.1\,\mathrm{deg/pixel}$, based on the original $12.8\!\times\!12.8\,{\rm deg^2}$ blocks, we generate $6.4\! \times\!6.4\,{\rm deg^2}$ inputs via two augmentations: (1) random cropping (boosting spatial diversity by $64^2$), (2) random masking with overlapping circular masks to mimic survey masks. The corresponding convergence field can then be reconstructed from the prepared shear using the $\mathtt{KS}$ algorithm.
• Figure 3: CSST-like photo-$z$ distribution. The red curve shows the photo-$z$ distribution with photo-$z$ uncertainties $\sigma(z)=\sigma_z(1+z)$, $\sigma_z=0.05$. Using this $z$-dependent kernel, the true-$z$ distribution (marked curve) is obtained by deconvolution. A mock true-$z$ galaxy catalog is generated assuming a galaxy number density of $26\,{\rm gal/arcmin^2}$ and intrinsic shape noise $\sigma_e = 0.288$. Incorporating photo-$z$ uncertainties, the mock photo-$z$ catalog is then constructed. To enhance the S/N of the WL signal, the photo-$z$ catalog is divided into 4 $z$-bins, each shown in a different color with its corresponding galaxy number density.
• Figure 4: Illustration of the sky-region partitioning into training, validation, and test sets. For each cosmology, the dataset contains 108 sky blocks, grouped in fours within the same declination region. Groups enclosed by red, blue, and white dashed boxes indicate the training, test, and validation sets, respectively, with no overlapping sky regions. Each block is a $128 \times 128$ mesh spanning $12.8 \times 12.8\,{\rm deg^2}$ and is randomly cropped to $6.4 \times 6.4\,{\rm deg^2}$ before input to the neural network. Each group of cropped blocks forms a sample, covering $163.84\,\mathrm{deg^2}$.
• Figure 5: Pipeline of shear measurement in each photo-$z$ bin including 4 steps to enhance the shear signal quality. When PCA processing is applied, the denoised shear field is denoted as $\bm{\gamma}^{\rm PCA}$; otherwise, the resulting field is denoted as $\bm{\gamma}^{\rm Avg}$.