  Next-generation cosmic microwave background (CMB) experiments will have lower
noise and therefore increased sensitivity, enabling improved constraints on
fundamental physics parameters such as the sum of neutrino masses and the
tensor-to-scalar ratio r. Achieving competitive constraints on these parameters
requires high signal-to-noise extraction of the projected gravitational
potential from the CMB maps. Standard methods for reconstructing the lensing
potential employ the quadratic estimator (QE). However, the QE performs
suboptimally at the low noise levels expected in upcoming experiments. Other
methods, like maximum likelihood estimators (MLE), are under active
development. In this work, we demonstrate reconstruction of the CMB lensing
potential with deep convolutional neural networks (CNN) - ie, a ResUNet. The
network is trained and tested on simulated data, and otherwise has no physical
parametrization related to the physical processes of the CMB and gravitational
lensing. We show that, over a wide range of angular scales, ResUNets recover
the input gravitational potential with a higher signal-to-noise ratio than the
QE method, reaching levels comparable to analytic approximations of MLE
methods. We demonstrate that the network outputs quantifiably different lensing
maps when given input CMB maps generated with different cosmologies. We also
show we can use the reconstructed lensing map for cosmological parameter
estimation. This application of CNN provides a few innovations at the
intersection of cosmology and machine learning. First, while training and
regressing on images, we predict a continuous-variable field rather than
discrete classes. Second, we are able to establish uncertainty measures for the
network output that are analogous to standard methods. We expect this approach
to excel in capturing hard-to-model non-Gaussian astrophysical foreground and
noise contributions.
