Dark Energy Survey Year 3 results: Simulation-based $w$CDM inference from weak lensing and galaxy clustering maps with deep learning. I. Analysis design

Abstract: Data-driven approaches using deep learning are emerging as powerful techniques to extract non-Gaussian information from cosmological large-scale structure. This work presents the first simulation-based inference (SBI) pipeline that combines weak lensing and galaxy clustering maps in a realistic Dark Energy Survey Year 3 (DES Y3) configuration and serves as preparation for a forthcoming analysis of the survey data. We develop a scalable forward model based on the CosmoGridV1 suite of N-body simulations to generate over one million self-consistent mock realizations of DES Y3 at the map level. Leveraging this large dataset, we train deep graph convolutional neural networks on the full survey footprint in spherical geometry to learn low-dimensional features that approximately maximize mutual information with target parameters. These learned compressions enable neural density estimation of the implicit likelihood via normalizing flows in a ten-dimensional parameter space spanning cosmological $w$CDM, intrinsic alignment, and linear galaxy bias parameters, while marginalizing over baryonic, photometric redshift, and shear bias nuisances. To ensure robustness, we extensively validate our inference pipeline using synthetic observations derived from both systematic contaminations in our forward model and independent Buzzard galaxy catalogs. Our forecasts yield significant improvements in cosmological parameter constraints, achieving $2-3\times$ higher figures of merit in the $\Omega_m - S_8$ plane relative to our implementation of baseline two-point statistics and effectively breaking parameter degeneracies through probe combination. These results demonstrate the potential of SBI analyses powered by deep learning for upcoming Stage-IV wide-field imaging surveys.

• The paper demonstrates a novel SBI framework that leverages deep learning to extract non-Gaussian features from DES Y3 maps.
• It combines weak lensing and galaxy clustering with advanced forward modeling and map-level compression to tighten constraints on key parameters like Ωm, S8, and w.
• Results show significant improvements in the figure of merit and reduced degeneracies compared to traditional two-point statistics, while maintaining robustness against systematic uncertainties.

Simulation-based $w$CDM Inference from Weak Lensing and Galaxy Clustering Maps with Deep Learning in DES Y3

Introduction and Motivation

This work presents a scalable simulation-based inference (SBI) framework for cosmological parameter estimation, combining weak gravitational lensing and galaxy clustering data from the Dark Energy Survey Year 3 (DES Y3). The methodology departs from traditional two-point statistics analyses by leveraging deep learning and forward modeling to efficiently extract non-Gaussian information from map-level data, thus aiming to tighten constraints on cosmological parameters, especially the matter density $\Omega_m$, structure amplitude $S_8$, and the dark energy equation-of-state parameter $w$.

Survey Configuration and Mock Data Generation

For realistic forecasts and validation, the analysis utilizes properties (e.g., redshift distributions, masking, number densities) of the DES Y3 Metacalibration source galaxy sample for weak lensing and the Maglim lens sample for galaxy clustering. Photometric redshift distributions and their uncertainties are implemented following DES Y3 calibration pipelines.

Figure 1: Normalized redshift distributions of DES Y3 sources (panel a) and lenses (panel b), with colored lines for base models and gray overlays reflecting photometric redshift uncertainties.

Synthetic map-level realizations are produced using the CosmoGridV1 $N$-body simulation suite, spanning a Sobol-sequence grid of $2,500$ $w$CDM cosmologies. This is complemented by baryonic corrections (via baryonification), intrinsic alignment modeling, and marginalization over nuisance parameters (shear and photo-$z$ biases, etc.), producing over $1,000,000$ deep mock observations.

Figure 3: Sampling of cosmological parameter space for CosmoGridV1, projected into the $\Omega_m$–$S_8$ plane.

Forward Modeling: Map-level Construction

CosmoGridV1 provides full-sky lensing and clustering lightcone projections, with DES-like masks and realistic tomographic binning. The pipeline generates weak lensing $\kappa$ maps by incorporating lensing, intrinsic alignment, and carefully constructed shape noise (the latter via randomized rotation of catalog ellipticities matching local galaxy densities). For clustering, linear bias models relate matter to galaxy counts, with Poisson sampling introduced to capture shot noise.

For tomography and masking, four non-overlapping DES Y3 footprints are extracted by rotation and HEALPix symmetries from full-sky maps, preserving pixel correspondence.

Figure 2: The DES Y3 footprint design, showing original (blue) and rotated (red) mask positions, and the extraction of four independent non-overlapping survey patches.

Extensive map smoothing and additional white noise are applied to enforce minimum scale cuts, ensuring model validity on small scales while enabling non-Gaussian feature retention on larger scales. These procedures are empirically validated against both analytic predictions and independent external simulations.

Figure 4: Comparison of original unsmoothed maps and the smoothed/noise-added versions used to enforce small-scale cuts and homogenize information content across tomographic bins.

Simulation-Based Inference Framework

The inference pipeline implements a Bayesian SBI strategy, employing deep neural networks as compression functions mapping high-dimensional map or power spectrum data to compact summaries optimized to retain mutual information about parameters. The training objective maximizes a tractable lower bound to the mutual information between summary and parameter vectors (variational mutual information maximization, VMIM).

Map-level compressions utilize graph convolutional neural networks (GCNNs, specifically DeepSphere), leveraging HEALPix structure to maintain geometric fidelity on the sky. The architecture operates on all redshift bins and probes jointly, capturing arbitrary cross-bin/probe correlations, and is trained on millions of highly realistic mock maps.

Following compression, neural likelihood estimation is performed using conditional normalizing flows, trained on the joint sample of compressed data and parameters, enabling nonparametric approximation of the map-level likelihood function. Posterior inference proceeds via MCMC sampling.

Validation Framework

Multiple rigorous validations are conducted:

1. Robustness to Model Misspecification: Using Buzzard catalogs (constructed with independent galaxy-halo connection models and different $N$-body code), cosmological parameters are recovered without significant bias, even in the presence of intentional discrepancies between forward and mock models.

Figure 7: Parameter recovery for individual probes and their combination on independent Buzzard mocks. All MAP estimates (blue) are within $< 0.5\sigma$ of ground truth (red) in the combined-probe case.

1. Systematic Stress-tests: The impact of large variations in baryonification strength, intrinsic alignment parameterization, source clustering bias, and $N$-body simulation fidelity is evaluated. All configuration shifts in the $\Omega_m$–$S_8$ plane are below the DES threshold of $0.3\sigma$, indicating strong robustness.

   Figure 5: Systematic error contamination impact, all shifts relative to the fiducial result are within the $0.3\sigma$ tolerance in the key $\Omega_m$–$S_8$ plane.

2. Posterior Predictive and Coverage Tests: Posterior predictive distributions for map-level summaries match independent mocks, and calibration curves (using HPD and TARP metrics) indicate nominal coverage properties for the high-dimensional posterior.

   Figure 6: Empirical validation of posterior coverage—calibration curves for HPD and TARP measures are consistent with expectation.

Results: Map-Level Deep Learning vs. Two-Point Statistics

The pipeline's constraining power is quantified via multiple axes:

• Map-level compression networks versus power spectrum-based baselines: Map-based analyses yield figures of merit (FoM, inverse area in parameter space) that are $2-3\times$ higher than two-point analyses, indicating significant retention of non-Gaussian information. For weak lensing alone, the map-level FoM is improved by $95\%$ over the baseline. For clustering, the improvement is $189\%$, and for combined probes, $143\%$.

Figure 8: Posterior contour comparison between map-level (deep learning) and power spectrum baseline for (left) weak lensing and (right) galaxy clustering. Significant tightening of posteriors is seen at map level.

• Degeneracy breaking: The addition of clustering information and higher-order map-level statistics reduces the well-known degeneracy between galaxy bias and $S_8$ (for clustering), and between $\Omega_m$ and $w$ (in probe combination), beyond what is possible via two-point statistics.
• Intrinsic alignment constraints: The intrinsic alignment parameter $A_{IA}$ does not benefit from the map-level strategy, with no significant improvement over the baseline, in contrast to prior findings using simpler IA models or scale cuts.
• Robust parameter recovery across probe configurations: Map-level compression reduces $1\sigma$ marginalized uncertainties by $30\%-50\%$ for principal cosmological parameters relative to two-point baseline, and probe combination further tightens constraints.

  Figure 12: Comparison of one-dimensional 68\% credible intervals for cosmological parameters across analysis strategies.

  

  Figure 9: Joint posterior distributions for all constrained parameters, contrasting individual and combined probes in map-level analysis.

Implications and Future Directions

The results establish that simulation-based deep learning approaches, when combined with realistic forward modeling, provide a robust mechanism for extracting higher-order, non-Gaussian information from LSS data at the map level. The demonstrated stability under systematic and model variations indicates suitability for realistic Stage-III analyses, and sets the stage for Stage-IV surveys (LSST, Euclid), where statistical precision will require full exploitation of non-Gaussian information.

Fully spherical GCNNs on HEALPix maps prove performant for compressed summary extraction from real survey footprints. The pipeline is extendable—higher-fidelity bias models (e.g., SHAM-based) for clustering, improved baryonification, and expanded IA parameterizations could further enhance constraining power.

On the AI method side, the work demonstrates the value of information-theoretic deep compression and high-dimensional simulation-based inference for cosmological summary statistics, reinforcing the shift away from handcrafted observables toward end-to-end learned summaries. These methods are broadly applicable to domains where analytic likelihoods are intractable but simulation-based forward models are feasible.

Conclusion

This study delivers a comprehensive simulation-based inference pipeline for cosmology, validated on challenging, realistic sets of mock DES Y3 data. By combining deep learning map-level compression and normalizing flow likelihood estimation, the framework achieves major gains in cosmological parameter constraints compared to traditional two-point statistics, especially in the presence of complex systematics and forward-modeling uncertainties. The rigorous validation scheme, including coverage and predictive tests, establishes the robustness of the approach. The methodology and infrastructure outlined here will be essential for fully exploiting the rich information encoded in next-generation cosmological surveys.