  We use convolutional neural networks (CNNs) and recurrent neural networks
(RNNs) to estimate the parameters of strong gravitational lenses from
interferometric observations. We explore multiple strategies and find that the
best results are obtained when the effects of the dirty beam are first removed
from the images with a deconvolution performed with an RNN-based structure
before estimating the parameters. For this purpose, we use the recurrent
inference machine (RIM) introduced in Putzky & Welling (2017). This provides a
fast and automated alternative to the traditional CLEAN algorithm. We obtain
the uncertainties of the estimated parameters using variational inference with
Bernoulli distributions. We test the performance of the networks with a
simulated test dataset as well as with five ALMA observations of strong lenses.
For the observed ALMA data we compare our estimates with values obtained from a
maximum-likelihood lens modeling method which operates in the visibility space
and find consistent results. We show that we can estimate the lensing
parameters with high accuracy using a combination of an RNN structure
performing image deconvolution and a CNN performing lensing analysis, with
uncertainties less than a factor of two higher than those achieved with
maximum-likelihood methods. Including the deconvolution procedure performed by
RIM, a single evaluation can be done in about a second on a single GPU,
providing a more than six orders of magnitude increase in analysis speed while
using about eight orders of magnitude less computational resources compared to
maximum-likelihood lens modeling in the uv-plane. We conclude that this is a
promising method for the analysis of mm and cm interferometric data from
current facilities (e.g., ALMA, JVLA) and future large interferometric
observatories (e.g., SKA), where an analysis in the uv-plane could be difficult
or unfeasible.
