Accelerating lensed quasar discovery and modeling with physics-informed variational autoencoders

TL;DR

This paper introduces VariLens, a physics-informed variational autoencoder that simultaneously detects strong lensing and infers SIE+$ abla_ ext{ext}$-type mass-model parameters from multiband images. Trained with a combination of real galaxy images and realistically simulated lensed-quasar systems, VariLens achieves millisecond inference on a CPU, delivering both lens probabilities and 11 physical parameters with uncertainties. On HSC data, the method recovers known lenses with good concordance for θ_E up to about $2''$ and identifies 42 high-quality lens candidates from an initial pool of tens of millions, demonstrating the approach’s effectiveness and scalability for future surveys like LSST and Euclid. The work highlights strong results for end-to-end lens discovery and rapid parameter inference, while also outlining limitations in shear estimation and redshift recovery, and it provides a practical pipeline for spectroscopic follow-up and high-resolution imaging to maximize scientific return.

Abstract

Strongly lensed quasars provide valuable insights into the rate of cosmic expansion, the distribution of dark matter in foreground deflectors, and the characteristics of quasar hosts. However, detecting them in astronomical images is difficult due to the prevalence of non-lensing objects. To address this challenge, we developed a generative deep learning model called VariLens, built upon a physics-informed variational autoencoder. This model seamlessly integrates three essential modules: image reconstruction, object classification, and lens modeling, offering a fast and comprehensive approach to strong lens analysis. VariLens is capable of rapidly determining both (1) the probability that an object is a lens system and (2) key parameters of a singular isothermal ellipsoid (SIE) mass model -- including the Einstein radius ($θ_\mathrm{E}$), lens center, and ellipticity -- in just milliseconds using a single CPU. A direct comparison of VariLens estimates with traditional lens modeling for 20 known lensed quasars within the Subaru Hyper Suprime-Cam (HSC) footprint shows good agreement, with both results consistent within $2σ$ for systems with $θ_\mathrm{E}<3$ arcsecs. To identify new lensed quasar candidates, we begin with an initial sample of approximately 80 million sources, combining HSC data with multiwavelength information from various surveys. After applying a photometric preselection aimed at locating $z>1.5$ sources, the number of candidates was reduced to 710,966. Subsequently, VariLens highlights 13,831 sources, each showing a high likelihood of being a lens. A visual assessment of these objects results in 42 promising candidates that await spectroscopic confirmation. These results underscore the potential of automated deep learning pipelines to efficiently detect and model strong lenses in large datasets.

Figures (18)

• Figure 1: Distribution of redshifts ($z_\mathrm{gal}$), stellar velocity dispersions ($\sigma_v$), Einstein radii ($\theta_\mathrm{E}$), and HSC $i$-band magnitudes ($i_\mathrm{HSC}$) for the galaxies used to simulate the lens systems. The orange histograms represent the mock lens configurations in all training, validation, and test datasets, while the mock lenses correctly identified by our classifier are highlighted with blue lines.
• Figure 2: Examples of mock lenses and other contaminants used for training the networks, with the inferred lens probability for each image indicated. By overlaying the multiply imaged source's light following an SIE+$\gamma_\text{ext}$ lens configuration onto a real galaxy image, we are able to construct realistic galaxy-quasar lens mocks.
• Figure 3: Simplified overview of the VariLens architecture. The networks include three main components: the encoder, decoder, and regressor. The input consists of a batch of 5-band HSC images, initially sized at $70\times70$ pixels. The batch size is flexible, with "None" indicating it can vary based on user specifications. These images are cropped, clipped, and rescaled to standardize pixel values before reaching the encoder. The encoder subsequently takes the preprocessed $64\times64$ pixel images and compresses them into a 64-dimensional latent representation. The decoder then reconstructs this latent representation back into the original cropped $64\times64$ pixel images. At the same time, the regressor estimates lens and source parameters, guiding the latent distribution to ensure it is physics-informed. Once the networks are fully trained, the decoder and regressor are removed and replaced by a single dense layer serving as the classification head. Transfer learning is then applied to fine-tune the classifier, optimizing it to effectively distinguish between lensing and non-lensing systems.
• Figure 4: Loss and accuracy curves over training epochs for the VariLens model. The left panel shows optimizations for the physics-informed VAE, while the right panel displays the one for the classifier module. The metrics, evaluated on the training and validation datasets, are depicted by the blue and orange lines, respectively. For the classifier, the dashed black line indicates the epoch when network fine-tuning begins. Prior to fine-tuning, the VariLens classifier appeared to perform worse on the training dataset compared to the validation samples. This could be due to the model not having fully converged or found the optimal weights at that stage.
• Figure 5: Image reconstruction examples. The original data containing mock lensed quasars, the reconstructed images predicted by VariLens, and the difference between them (i.e., residuals) are shown. These HSC $grz$ images originate from sources within the test dataset.