DESI Strong Lens Foundry

• DESI Strong Lens Foundry is a multi-pronged research program that systematically discovers and confirms strong gravitational lenses using wide-area imaging and massive spectroscopic surveys.
• It deploys state-of-the-art machine learning and high-resolution imaging, achieving high success rates and robust candidate selection through ensemble models and visual grading.
• The project uses GPU-accelerated Bayesian modeling to accurately determine lens mass profiles and derive key cosmological parameters such as the Hubble constant and dark matter properties.

The DESI Strong Lens Foundry is a comprehensive, multi-pronged research program targeting the discovery, confirmation, and modeling of strong gravitational lens systems in the era of large-scale imaging and spectroscopic surveys. Rooted in the imaging data from the DESI Legacy Imaging Surveys and leveraging massive spectroscopic resources such as the Dark Energy Spectroscopic Instrument (DESI), the Foundry aims to systematically identify, spectroscopically confirm, and characterize thousands of strong lens systems across galaxy, group, and cluster mass scales. The project employs state-of-the-art machine learning, multifiber spectroscopy, high-resolution space- and ground-based imaging, and advanced, GPU-accelerated Bayesian modeling, yielding a dataset that is critical for probing the structure of galaxies, the nature of dark matter, and key cosmological parameters such as the Hubble constant.

1. Machine Learning-Based Lens Discovery

The foundational step of the DESI Strong Lens Foundry is the systematic search for lens candidates in the DESI Legacy Imaging Surveys, spanning up to 19,000 deg² with multi-band grz imaging to z_AB ≈ 22.5. The primary tool is a deep residual neural network (ResNet) architecture, trained directly on observed images of known lens systems and nonlenses (excluding simulated data, to match the survey characteristics) (Huang et al., 2019, Huang et al., 2020, Storfer et al., 2022, Inchausti et al., 27 Aug 2025). Training sets explicitly include rare configurations, high-quality reference lenses, and a large set of nonlenses to optimize the background/foreground ratio (as high as 100:1 in DR10 analysis).

The workflow proceeds as follows:

• Cutout images (101×101 pixels, ∼26″) centered on extragalactic, non-PSF classified sources (SER, DEV, REX, EXP) with z_AB < 20.0 and sufficient multiband coverage are extracted.
• The ResNet (and, in later iterations, EfficientNet) architectures minimize the cross-entropy loss function:

$$L_{CE} = -\sum_i \left[ y_i \log(\hat{y}_i) + (1-y_i) \log(1-\hat{y}_i) \right]$$

where $y_i$ is the binary label and $\hat{y}_i$ the model output for image $i$ (Storfer et al., 2022, Inchausti et al., 27 Aug 2025).

• Ensemble modeling aggregates the outputs of differently parameterized networks, increasing robustness and boosting area under the ROC curve (AUC up to 0.9997 on validation).
• The top-scoring cutouts (e.g., top 0.01% by neural net probability) are visually inspected and graded into Grades A, B, and C according to arc clarity and lens morphology (Huang et al., 2019).

Using this method, discovery runs have yielded:

• 335 candidates in DR8 (Huang et al., 2019)
• 1,210 in DR8/9 (Huang et al., 2020)
• 1,895 in DR9 (Storfer et al., 2022)
• 811 in DR10 (Inchausti et al., 27 Aug 2025) yielding a total of at least 3,868 new candidates in the DR8–DR10 data.

2. Spectroscopic Confirmation and High-Resolution Imaging

Spectroscopic confirmation is essential for establishing lens candidates as genuine lensing systems, requiring secure measurements of both the lens (deflector) and background source redshifts. The Foundry executes this via:

• DESI Strong Lensing Secondary Target Program: Multiplexed DESI spectroscopy provides lens and source redshifts with >98% success rate for lens galaxies, confirming 20 of 73 EDR candidates (w/ more awaiting further observations). Both absorption (lens: Ca HK, G-band, 4000 Å break) and emission ([O II], Hβ, [O III], Lyα for sources) lines are used. Candidate source redshifts range up to $z_s > 3$ (Huang et al., 22 Sep 2025).
• Keck NIRES Follow-up: Near-IR Keck/NIRES spectroscopy measures high-z source redshifts (1.7 < $z_s$ < 3.3) when emission lines are shifted out of DESI’s optical range. PypeIt-based reduction and custom extractions are used (Agarwal et al., 22 Sep 2025).
• VLT/MUSE Integral Field Spectroscopy: MUSE provides spatially resolved spectroscopy, enabling simultaneous extraction of spectra from lens and multiple arcs. 75 candidates observed, confirming both lens and source redshifts in 48 systems, including multiple-source-plane and cluster/group-scale lenses, with redshifts up to $z_s \sim 2.45$ (Lin et al., 22 Sep 2025).

High-resolution imaging by HST (WFC3, F140W), as in the Foundry’s SNAP program (GO-15867, PI: Huang), guarantees all visually selected high-probability candidates display unambiguous lensing morphologies—i.e., all 51 HST-observed candidates were confirmed lenses (Huang et al., 5 Feb 2025).

3. Automated Bayesian Lens Modeling

Comprehensive mass modeling is performed using the GPU-accelerated GIGA-Lens Bayesian pipeline, which enables fully forward-modeling of the image and light profile, integrating all instrumental effects and uncertainties with Hamiltonian Monte Carlo sampling. The pipeline allows:

• Flexible elliptical power-law (EPL) lens mass distributions, parameterized as

$$\kappa(x, y) = \frac{3-\gamma}{2}\left(\frac{\theta_E}{\sqrt{q x^2 + y^2/q}}\right)^{\gamma-1}$$

where $\theta_E$ is the Einstein radius, $q$ is axis ratio, and $\gamma$ the 3D mass slope (Huang et al., 5 Feb 2025).

• Additional components (multipole mass structures, external shear, Sersic light profiles, neighboring galaxies) as needed; typical fits span 31–41 parameters to model both mass and light.
• Fully automatic differentiation for gradient computation, enabling efficient exploration of high-dimensional posterior distributions.
• MAP optimization, surrogate SVI covariance estimates, and HMC sampling on multi-GPU hardware deliver convergence for complex systems within several hours.

This approach has enabled, e.g., precise modeling of DESI-165.4754-06.0423, with minimal residuals between observed and reconstructed arcs (Huang et al., 5 Feb 2025), as well as Einstein Cross systems (DESI-253.2534+26.8843) with precise measurement of Einstein radius and inferred velocity dispersion, e.g.,

$$\theta_E = 4\pi \left(\frac{\sigma_{\rm SIE}}{c}\right)^2 \frac{D_{\rm L1{-}s}}{D_s}$$

yielding, e.g., $\sigma = 379 \pm 2$ km s⁻¹ (Cikota et al., 2023).

4. Complementary Discovery Techniques

The DESI Strong Lens Foundry incorporates and/or inspires several additional discovery pipelines:

• Pair-wise Spectroscopic Search: A novel approach leveraging the high fiber density in DESI, matching “friend-of-friend” spectral pairs separated by <3″ with significantly discrepant redshifts ($z_{\rm max}/z_{\rm min} > 1.3$), then cross-validating with imaging cutouts and estimated Einstein radii. This yielded 2,046 conventional lens candidates (1,906 new), plus 318 new “dimple lenses” plausibly associated with dwarf-galaxy-scale lenses, allowing probes of halo mass functions for $M_{\rm Halo} \lesssim 10^{13} M_\odot$ (Hsu et al., 19 Sep 2025).
• Catalogue-Driven Quasar Lens Search: By grouping >24 million quasar candidates via a HEALPix-based friend-of-friends algorithm, refining candidates via color-similarity and quasar probability scores, and visual grading, a catalogue of 620 new lensed quasar candidates (101 Grade A) was released. These are central for time-delay cosmography and H₀ measurements (He et al., 2023).
• Retrospective Transient Searches: Automated pipelines using difference imaging and spatial–temporal grouping on DESI image stacks identified multiple strongly lensed supernovae, including candidates with Einstein radii of ~1.5″, critical for independent constraints on cosmological parameters via time-delay measurements (Sheu et al., 2023).

5. Scientific Impact and Legacy

The strong lens sample produced by the DESI Strong Lens Foundry has deep implications for a range of scientific inquiries:

• Cosmology: Large, well-characterized strong lens samples enable time-delay measurements in lensed supernovae and quasars to independently constrain H₀ and probe dark energy via the distance ratio dependence of the Einstein radius and time delays.
• Dark Matter Substructure: High-fidelity mass models and perturbed arcs in the Foundry sample are used to probe the subhalo mass function and thus to test cold dark matter predictions, especially in the regime $M_{\rm Halo} \lesssim 10^{13} M_\odot$ (Hsu et al., 19 Sep 2025).
• Galaxy and Cluster Mass Profiles: Modeling galaxy- to cluster-scale lenses, including complex environments with multiple source planes, provides robust tests of the baryon–dark matter interplay, cluster structure, and evolution over cosmic time (Sheu et al., 19 Aug 2024).
• General Relativity Constraints: The LaStBeRu (Last Stand Before Rubin) database, integrating DESI Legacy imaging and spectroscopy, enables constraints on the parameterized Post-Newtonian parameter $\gamma_{\rm PPN}$ by comparing lensing-based mass and stellar-dynamical mass estimates through velocity dispersions. Constraints on $\gamma_{\rm PPN}$ are found to be consistent with GR at the 1σ level (Oliveira et al., 11 Sep 2025).

6. Future Directions and Scalability

The Foundry is designed for scalability and adaptability to future data. Ongoing/future efforts include:

• Expansion of discovery pipelines: Integration of hierarchical visual Transformer architectures and meta-learner ensembles for further gains in completeness and purity, domain adaptation for survey variations, and hybrid catalogue+image-based searches (Li et al., 2 Apr 2024, Inchausti et al., 27 Aug 2025).
• Automated, GPU-accelerated lens modeling: Routine exploitation of large-lens samples as facilities such as LSST, Euclid, and Roman Space Telescope come online, targeting >10⁴ confirmed lenses.
• Spectroscopic confirmation at scale: Anticipated final DESI DR will provide ~50 million spectra, facilitating mass confirmation of hundreds to thousands of strong lens systems via cross-matching with imaging discoveries (Shu et al., 22 May 2025).
• Training sets and simulators: Spectroscopically confirmed lens and non-lens samples from DESI/HST/MUSE form the foundation for robust machine learning training, essential for high-purity selections in future surveys, as highlighted in the Euclid Q1 Discovery Engine and LaStBeRu projects (Collaboration et al., 19 Mar 2025, Oliveira et al., 11 Sep 2025).
• Extension to time-variable sources and joint modeling frameworks: Future pipelines will directly model lenses with variable sources, necessary for time-delay cosmography and the calibration of independent cosmological probes.

The DESI Strong Lens Foundry represents an overview of deep learning-based data mining, massive multiplexed spectroscopy, high-resolution space and ground-based imaging, and end-to-end Bayesian modeling. Its legacy is the creation of the largest, most robustly confirmed, and most precisely modeled sample of strong gravitational lenses in the pre-LSST era, forming the empirical groundwork for the next generation of astrophysical and cosmological analyses.