Modeling lens potentials with continuous neural fields in galaxy-scale strong lenses

Strong gravitational lensing is a unique observational tool for studying the dark and luminous mass distribution both within and between galaxies. Given the presence of substructures, current strong lensing observations demand more complex mass models than smooth analytical profiles, such as power-law ellipsoids. In this work, we introduce a continuous neural field to predict the lensing potential at any position throughout the image plane, allowing for a nearly model-independent description of the lensing mass. We applied our method to simulated Hubble Space Telescope imaging data containing different types of perturbations to a smooth mass distribution: a localized dark subhalo, a population of subhalos, and an external shear perturbation. Assuming knowledge of the source surface brightness, we used the continuous neural field to model either the perturbations alone or the full lensing potential. In both cases, the resulting model was able to fit the imaging data, and we were able to accurately recover the properties of both the smooth potential and the perturbations. Unlike many other deep-learning methods, ours explicitly retains lensing physics (i.e., the lens equation) and introduces high flexibility in the model only where required, namely, in the lens potential. Moreover, the neural network does not require pretraining on large sets of labeled data and predicts the potential from the single observed lensing image. Our model is implemented in the fully differentiable lens modeling code HERCULENS.