The source paper (Ding et al. 2025, published as A&A 712, A49, 2026) introduced a shear-to-cosmology pipeline that maps weak-lensing shear fields directly to cosmological parameters, combining a Transformer-based field-level-inference (FLI) feature extractor with neural-posterior-estimation simulation-based inference (SBI) and a blind, training-free PCA shear denoiser. On CSST-like mocks containing only galaxy shape noise and photo-z binning uncertainty, it reports roughly twice the (Ωm,σ8)(\Omega_{\rm m},\sigma_8) figure of merit (FoM) relative to Kaiser–Squires convergence-based inference and a 36.4% FoM gain over shear two-point statistics. That gain was measured in an idealized regime: the pipeline omits essentially all observational and astrophysical systematics — PSF residuals, shear measurement biases, mean-redshift biases, intrinsic alignments, source clustering, magnification, reduced shear, and baryonic feedback — and was tested at reduced angular resolution, sky area, and simulation fidelity. The open problem is the deployment-readiness of reconstruction-free shear-to-cosmology inference: forward-model and marginalize the full systematics set within the shear-domain FLI+SBI framework, characterize parameter biases induced by the PCA denoiser and by the choice of convergence reconstruction, and validate the pipeline at Stage-IV survey fidelity. Adjacent frameworks have already completed the analogous program — DES Year-3 map-level SBI analyses forward-model these systematics on real data, and explicit Bayesian field-level inference includes intrinsic alignments and baryons — so the surviving open core is specifically the shear-domain, learned-compression SBI variant and whether its claimed non-Gaussian information advantage survives realistic conditions.

Background

Gravitational lensing by the large-scale structure of the Universe coherently distorts the shapes of distant galaxies. The observable is the cosmic shear γ=(γ1,γ2)\gamma=(\gamma_1,\gamma_2), a two-component spin-2 field on the sky; its weighted line-of-sight projection of the matter overdensity is the convergence κ\kappa. On the flat sky the two fields are related by a fixed Fourier-space kernel, so the convergence can be reconstructed from the shear by the Kaiser–Squires (KS) inversion (Kaiser and Squires, 1993), the standard mass-mapping step of weak-lensing (WL) analyses. Conventional analyses compress the field into two-point statistics such as shear correlation functions; these capture all statistical information only for a Gaussian field, whereas nonlinear gravitational collapse at late times makes the low-redshift lensing field distinctly non-Gaussian. This motivates extracting higher-order and map-level information, which next-generation ('Stage-IV') WL surveys — the Vera C. Rubin Observatory/LSST, Euclid, Roman, and the Chinese Space Station Telescope (CSST) — will measure with far greater precision than current surveys.

Field-level inference (FLI) is the approach of constraining cosmology by comparing the full observed field, or learned summaries of it, against a forward model of the field, rather than against hand-designed low-order statistics (Leclercq, 2025). In the implicit, simulation-based-inference (SBI) variant, a neural network compresses the data while a conditional density estimator — here a normalizing flow trained with neural posterior estimation (NPE) — approximates the posterior p(θ∣x)p(\theta|x) from parameter–simulation pairs. The source paper (Ding et al., 2025) built exactly such a shear-to-cosmology pipeline for CSST-like mock catalogs: (i) a blind, training-free denoising of the shear field along the redshift direction using principal component analysis (PCA), exploiting that the lensing signal is correlated across redshift bins while per-galaxy shape noise is not; (ii) a Transformer-based network that extracts informative features from multi-redshift shear maps; and (iii) NPE mapping those features to (Ωm,σ8)(\Omega_{\rm m},\sigma_8). It reports approximately twice the constraining FoM relative to inference on KS-reconstructed convergence maps, and a 36.4% FoM improvement over shear two-point correlations.

Real WL analyses, however, must control a standard set of observational and astrophysical systematics, none of which (beyond shape noise and photo-z binning) the source pipeline includes: point-spread-function (PSF) residuals, i.e. imperfectly modeled instrumental image blur that leaks into measured galaxy shapes; shear measurement biases, i.e. multiplicative and additive calibration errors in the shape estimator; mean-redshift and photometric-redshift (photo-z) biases, i.e. errors in the galaxy redshift distributions that set the lensing kernel; intrinsic alignments (IA), i.e. correlations of galaxy orientations with the gravitational tidal field and with each other that contaminate the lensing-only signal; source clustering, i.e. correlations between lensed source positions and the foreground density field; magnification, i.e. lensing-induced fluctuations in source number density; reduced shear, i.e. the fact that the observable is g=γ/(1−κ)g=\gamma/(1-\kappa) rather than γ\gamma itself; and baryonic feedback, i.e. redistribution of gas by AGN and supernova feedback that alters the small-scale matter distribution. In addition, the source study used reduced angular resolution and effective sky area relative to Stage-IV surveys, and its ray-tracing simulations had unsynchronized timesteps across cosmologies, forcing coarser redshift sampling.

The analogous systematics-inclusion program has been completed in adjacent frameworks. On Dark Energy Survey (DES) Year-3 real data, map-level SBI analyses forward-model the dominant systematics: wavelet-phase-harmonic, scattering-transform, and moment statistics of convergence maps (Gatti et al., 2024) forward-model masks, noise variations, source clustering, IA, and shear and redshift calibration; hybrid map-level statistics (Williamson et al., 2026) forward-model the mask, photo-z uncertainties, IA, multiplicative shear bias, source clustering, and non-Gaussian shape noise, validated against baryonic feedback; persistent-homology statistics (Prat et al., 2025) are validated against baryonic feedback; and a deep-learning pipeline combining weak-lensing and galaxy-clustering maps (Thomsen et al., 2025) marginalizes over IA, baryonic, photo-z, and shear-bias nuisances in a ten-dimensional parameter space. In the explicit Bayesian FLI framework, BORG-WL includes IA (tidal alignment and tidal torquing models) and baryon feedback at field level (Porqueres et al., 2023), while the catalog-to-cosmology pipeline Miko (Zhou et al., 2023) controls field-level analysis systematics such as aliasing, Fourier mode-coupling, and density-induced shape noise to the 2% level but explicitly defers IA, photo-z, and PSF effects. Recent method work has addressed the simulation-cost side of scaling field-level inference (multifidelity SBI with 60–100 high-fidelity simulations, Saoulis et al., 2026) and compared implicit and explicit FLI with coverage tests (Omori et al., 2026). All of these operate on convergence maps, catalogs, or explicit likelihoods; none validates the reconstruction-free shear-domain FLI+SBI framework of the source paper under the full systematics set.

Problem Statement

The open problem is the deployment-readiness of the shear-to-cosmology field-level simulation-based-inference framework for Stage-IV weak-lensing surveys. The source paper demonstrated, on CSST-like mocks containing only galaxy shape noise and photo-z binning uncertainty, that inference directly on multi-redshift shear fields yields roughly twice the (Ωm,σ8)(\Omega_{\rm m},\sigma_8) figure of merit (FoM) of KS-convergence-based inference; the open question is whether this reconstruction-free, non-Gaussian-information advantage survives realistic survey conditions. An answer must, as a single coherent objective with jointly supporting components: (i) forward-model and marginalize the full set of dominant weak-lensing systematics in the shear-domain pipeline — PSF residuals, shear measurement biases, mean-redshift and photo-z biases, intrinsic alignments, source clustering, magnification, reduced shear, and baryonic feedback — with their nuisance parameters sampled in the SBI posterior rather than fixed to truth; (ii) characterize and control the parameter biases induced by the blind PCA redshift-direction denoiser (and, if it is replaced or augmented, e.g. by wavelet or blind-source-separation denoising, bias-test the replacement); (iii) quantify how much of the idealized FoM gain survives each systematic, including the reconstruction-dependence of the convergence-based baseline (Kaiser–Squires versus Wiener, wavelet, Bayesian, or learned reconstructions); and (iv) demonstrate the above at Stage-IV-like angular resolution, effective sky area, and simulation fidelity, with realistic partial-sky ray-traced mock data that include image-level systematics. The completion boundary is the joint delivery of components (i)–(iv): an end-to-end validated analysis on realistic Stage-IV-like mocks, with the parameter biases induced by the included systematics, by the denoiser, and by the convergence-reconstruction choice quantified; the source paper itself identifies more realistic mock datasets — based on high-resolution N-body simulations, partial-sky ray-tracing, and realistic image simulations — as the way to address its reduced resolution, effective sky area, and omitted systematics, and a comparable validation pattern already exists in the DES Year-3 map-level SBI program.

References

  1. Jiacheng Ding, Chen Su, Ji Yao, Le Zhang, Huanyuan Shan (2025). The Shear-to-Cosmology Paradigm I. Hybrid Field-Level and Simulation-Based Framework for Weak Lensing Surveys. arXiv:2511.22851; published as Astronomy & Astrophysics 712, A49 (2026), DOI 10.1051/0004-6361/202658859. https://arxiv.org/abs/2511.22851
  2. Nick Kaiser, Gordon Squires (1993). Mapping the dark matter with weak gravitational lensing. DOI 10.1086/172297. https://doi.org/10.1086/172297
  3. Natalia Porqueres, Alan Heavens, Daniel Mortlock, Guilhem Lavaux, T. Lucas Makinen (2023). Field-level inference of cosmic shear with intrinsic alignments and baryons. arXiv:2304.04785. https://arxiv.org/abs/2304.04785
  4. Alan Junzhe Zhou, Xiangchong Li, Scott Dodelson, Rachel Mandelbaum (2023). Accurate field-level weak lensing inference for precision cosmology. arXiv:2312.08934; published as Physical Review D 110, 023539 (2024), DOI 10.1103/PhysRevD.110.023539. https://arxiv.org/abs/2312.08934
  5. M. Gatti, G. Campailla, N. Jeffrey, L. Whiteway, A. Porredon, J. Prat, et al. (2024). Dark Energy Survey Year 3 results: simulation-based cosmological inference with wavelet harmonics, scattering transforms, and moments of weak-lensing mass maps. II. Cosmological results. arXiv:2405.10881; published as Physical Review D 111, 063504 (2025), DOI 10.1103/PhysRevD.111.063504. https://arxiv.org/abs/2405.10881
  6. A. Thomsen, J. Bucko, T. Kacprzak, V. Ajani, J. Fluri, A. Refregier, et al. (2025). Dark Energy Survey Year 3 results: Simulation-based wCDM inference from weak lensing and galaxy clustering maps with deep learning: Analysis design. arXiv:2511.04681. https://arxiv.org/abs/2511.04681
  7. J. Williamson, T. L. Makinen, N. Porqueres, N. Jeffrey, A. Heavens, M. Gatti, et al. (2026). Dark Energy Survey Year 3 results: optimized wCDM simulation-based inference with weak lensing map-level hybrid statistics. arXiv:2606.11309. https://arxiv.org/abs/2606.11309
  8. J. Prat, M. Gatti, C. Doux, P. Pranav, C. Chang, N. Jeffrey, et al. (2025). Dark Energy Survey Year 3 results: wCDM cosmology from simulation-based inference with persistent homology on the sphere. arXiv:2506.13439; published in Monthly Notices of the Royal Astronomical Society, DOI 10.1093/mnras/staf2152. https://arxiv.org/abs/2506.13439
  9. Yuuki Omori, Justine Zeghal, Chihway Chang, François Lanusse, Laurence Perreault-Levasseur (2026). Towards Practical Field-Level Inference for Weak Lensing. arXiv:2606.12255. https://arxiv.org/abs/2606.12255
  10. Alex A. Saoulis, Kiyam Lin, Niall Jeffrey, Maximilian von Wietersheim-Kramsta, Davide Piras, Alessio Spurio Mancini, Ana M. G. Ferreira, Benjamin Joachimi (2026). Field-level weak lensing cosmology with <100 simulations using multifidelity simulation-based inference. arXiv:2606.23346. https://arxiv.org/abs/2606.23346
  11. Sophie Hoyland, Daniela Saadeh, Kazuya Koyama, Harry Desmond (2026). Disentangling modified gravity and galaxy bias with field-level inference. arXiv:2607.03514. https://arxiv.org/abs/2607.03514
  12. Florent Leclercq (2025). Field-level inference in cosmology. arXiv:2509.13435. https://arxiv.org/abs/2509.13435
  13. Sneh Pandya, Jonathan Blazek (2026). Differentiable Stochastic Halo Occupation Distribution with Galaxy Intrinsic Alignments. arXiv:2602.04977, DOI 10.33232/001c.159889. https://arxiv.org/abs/2602.04977