Automating strong galaxy-scale gravitational lens modelling with neural networks

Strong galaxy-scale gravitational lensing provides a powerful means of studying galaxy formation, constraining cosmology and understanding the evolution of large-scale structure. The presence of a foreground lensing galaxy deflects the light rays of a background source into multiple images, with their configuration dependent upon the lens mass distribution. Modelling of this distribution to reproduce the lensed images not only aids in measuring the dark matter content of the foreground galaxy, but allows for the reconstruction of the background source in order to study high-redshift galaxy populations. Modelling is typically performed by relatively slow parametric parameter-fitting techniques requiring manual inspection. However, upcoming large-scale surveys like the Legacy Survey of Space and Time (LSST) and Euclid will discover tens of thousands of strong lenses, with this vast quantity driving the growing use of automated machine learning for both identifying and modelling such systems extremely quickly. Convolutional neural networks (CNNs) can extract information from lensed images in order to predict parameters of the lens mass model, but require large simulated data sets for training and testing. In this thesis, I explore the effectiveness of deep learning CNNs for estimating strong galaxy-scale lens mass model parameters when applied to upcoming wide-field survey data, investigating the practicalities they face and comparing and combining them with conventional modelling methods. I construct a CNN and train it on my own simulated lensing images with the imaging characteristics of the Euclid VIS band, LSST r-band, and LSST gri multiband. The CNN is trained to predict parameters of a smooth singular isothermal ellipsoid (SIE) projected mass profile that would best fit the observed image. Multiple aspects of this method are investigated, beginning with a comparison of its accuracy and reliability when applied to the survey data sets. The impact of multiband imaging is analysed, as well as the impact of lens light subtraction commonly performed by conventional modelling techniques. I show that for images including lens galaxy light, the CNN recovers the lens model parameters with an acceptable accuracy, with precision improved on average by 34 ± 5 per cent when lens light is subtracted. Additionally, the inclusion of multiband data improves performance regardless of lens light subtraction. While similar accuracies and precision are obtained for single epoch Euclid VIS and LSST r-band data sets, adding g- and i-band images to the latter increases precision by 24 ± 2 per cent without lens light and by 20 ± 2 per cent with lens light. I also examine the gains in performance through stacking images, and the impact of lens mass-light alignment. For the latter, when orientation and ellipticity of the lens light profile are allowed to differ from those of its mass profile, just as with real galaxies, the network performs most consistently when trained with a moderate amount of scatter between the two profiles. I next seek ways of improving the method for application to real images, starting by implementing an existing technique to create a new Bayesian CNN that can predict both model parameters and their uncertainties. New data sets are then simulated for training and testing the network, allowing the network to either predict parameters of the SIE profile or predict those of the more general elliptical power law profile. To examine how the CNN performs at fitting these profiles to more complex mass models, these data sets feature a range of increasingly realistic lensing systems, from smooth parametric mass and light profiles to featuring real background sources, complex hydrodynamically-generated foreground mass distributions and line-of-sight structure. In order to assess the suitability of the Bayesian CNN as a whole, I compare its performance when tested on these data sets to that of a conventional fitting method: the semilinear inversion technique PyAutoLens. In addition, I present a method for combining the network with such inversion methods where the CNN provides initial priors on the latter's parameters. Across the test sets, I find that the CNN achieves errors 19 ± 22 per cent lower than when applying PyAutoLens blindly. Compared to PyAutoLens alone, the initial centring of its priors on CNN-predicted parameters instead achieves 27 ± 11 per cent lower errors. If the prior widths are additionally initialised according to CNN-predicted Bayesian uncertainties, errors are reduced further to 37 ± 11 per cent as the uncertainties help it to avoid local minima in parameter space, with errors also 17 ± 21 per cent lower than the CNN by itself. While the CNN is undoubtedly the fastest modelling method, the combination of the two increases the speed of conventional fitting alone by a factor of 1.73 and 1.19 with and without CNN-predicted uncertainties, respectively. This, combined with greatly improved precision, highlights the benefits obtainable through combining neural networks with conventional techniques in order to achieve an efficient automated modelling approach. I finish off this thesis by discussing the scientific applications requiring such an approach, and examining how tightly these methods can constrain cosmological parameters through the modelling of double source plane lenses to aid in our understanding of the Universe