  Cosmic polarization rotation, which may result from parity-violating new
physics or the presence of primordial magnetic fields, converts $E$-mode
polarization of the cosmic microwave background (CMB) into $B$-mode
polarization. Anisotropic cosmic polarization rotation leads to statistical
anisotropy in CMB polarization and can be reconstructed with quadratic
estimator techniques similar to those designed for gravitational lensing of the
CMB. At the sensitivity of upcoming CMB surveys, lensing-induced $B$-mode
polarization will act as a limiting factor in the search for anisotropic cosmic
polarization rotation, meaning that an analysis which incorporates some form of
delensing will be required to improve constraints on the effect with future
surveys. In this paper we extend the ResUNet-CMB convolutional neural network
to reconstruct anisotropic cosmic polarization rotation in the presence of
gravitational lensing and patchy reionization, and we show that the network
simultaneously reconstructs all three effects with variance that is lower than
that from the standard quadratic estimator nearly matching the performance of
an iterative reconstruction method.
