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.
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