Euclid Quick Data Release (Q1). LEMON -- Lens Modelling with Neural networks. Automated and fast modelling of Euclid gravitational lenses with a singular isothermal ellipsoid mass profile

TL;DR

LEMON tackles the demand for automated, fast, and uncertainty-aware modelling of strong gravitational lenses in the Euclid era by deploying a Bayesian neural network based on ResNet (LEMON) to recover both the mass distribution (SIE with external shear) and the foreground light (Sérsic) of lens galaxies. Trained on 100000 mock lenses and tested on Euclidised HST lenses and real Q1 data, LEMON outputs parameter posteriors for $R_{ extrm{Ein}}$, ellipticities, $R_{ extrm{e}}$, $n_{ extrm{lens}}$, $m_{ extrm{lens}}$, and source positions, with calibrated total uncertainties via Platt-scaling. Across mock tests and real data, Einstein radii and light ellipticities are recovered with high fidelity, while the Sérsic index remains challenging; real data show reasonable agreement with literature and PyAutoLens results, especially for $R_{ extrm{Ein}}$, light ellipticities, and magnitudes. Importantly, using LEMON predictions as initial conditions for gradient-based PyAutoLens inference yields up to ~26× speed-ups, enabling scalable lens modelling for the expected ~10^5 lenses from Euclid and contributing to robust inferences of dark matter content and stellar populations. The work thus provides a robust, fast, and calibratable pathway toward automated lens modelling in large surveys, with clear directions for broadened mass models and enhanced preprocessing.

Abstract

The Euclid mission aims to survey around 14000 deg^{2} of extragalactic sky, providing around 10^{5} gravitational lens images. Modelling of gravitational lenses is fundamental to estimate the total mass of the lens galaxy, along with its dark matter content. Traditional modelling of gravitational lenses is computationally intensive and requires manual input. In this paper, we use a Bayesian neural network, LEns MOdelling with Neural networks (LEMON), to model Euclid gravitational lenses with a singular isothermal ellipsoid mass profile. Our method estimates key lens mass profile parameters, such as the Einstein radius, while also predicting the light parameters of foreground galaxies and their uncertainties. We validate LEMON's performance on both mock Euclid datasets, real lenses observed with Hubble Space Telescope (HST), and real Euclid lenses, demonstrating the ability of LEMON to predict parameters of both simulated and real lenses. Results show promising accuracy and reliability in predicting the Einstein radius, mass and light ellipticities, effective radius, Sérsic index, lens magnitude, and unlensed source position for simulated lens galaxies. The application to real data, including the latest Quick Release 1 strong lens candidates, provides encouraging results in the recovery of the parameters for real lenses. We also verified that LEMON has the potential to accelerate traditional modelling methods, by giving to the classical optimiser the LEMON predictions as starting points, resulting in a speed-up of up to 26 times the original time needed to model a sample of gravitational lenses, a result that would be impossible with randomly initialised guesses. This work represents a significant step towards efficient, automated gravitational lens modelling, which is crucial for handling the large data volumes expected from Euclid.

Figures (21)

• Figure 1: Distribution of mass and light parameters for the mock lenses.
• Figure 2: $20\arcsec \times 20\arcsec$ original VIS images of some examples of mock lenses used for training LEMON.
• Figure 4: Recovery plot of the parameters of mock lenses, showing how well the predicted model parameters from LEMON ($y$ co-ordinate) reproduce the corresponding true value ($x$ co-ordinate), for each lens of the test set (blue points). The ideal recovery line is shown as a dashed black line. The median trend of the scatter plots, along with the respective scatters associated with the 16th and 84th percentiles, are shown as red points and bars, respectively. For each panel, we also report the respective cumulative metrics. The bottom two rows of each parameter show the bias and the NMAD, respectively, as defined in Sect.\ref{['sec:metrics']}, as a function of the true value of the parameters estimated by LEMON. For clarity, we have plotted only 5000.0 random points from the test set.
• Figure 5: Random selection of 20 $10\arcsec \times 10\arcsec$ cut-outs of simulated lenses taken from the test set. Red circles show the best predictions for the Einstein radius from LEMON, with corresponding 16th and 84th percentiles shown with dashed red circles. Yellow circles show the true values for the Einstein radii. Predictions and true values are very similar, so in some cases the corresponding circles completely overlap.
• Figure 6: Calibrated relative uncertainty as a function of the true value of the lens parameters. For the ellipticity components, lens magnitude, and source co-ordinates, we consider the absolute uncertainty. For clarity, we plotted only 5000.0 random points. The median trends of the scatter plots, along with the respective scatters associated with the 16th and 84th percentiles, are shown as red points and bars, respectively.