Euclid Quick Data Release (Q1): XXXI. LEMON ─ LEns MOdelling with Neural networks. Automated and fast modelling of Euclid gravitational lenses with singular isothermal ellipsoid mass profile

The Euclid mission aims to survey around 14 000 deg2 of extragalactic sky, providing around 105 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) that have been degraded to match observations with the same depth of the Euclid Wide Survey, 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. Moreover, LEMON can be used to cross-validate results from the traditional modelling methods, and thus has the potential to reduce the failure rate of the Euclid modelling pipeline. This work represents a significant step towards efficient, automated gravitational lens modelling, which is crucial for handling the large data volumes expected from Euclid.