Fast Wiener filtering of CMB maps with Neural Networks
  We show how a neural network can be trained to Wiener filter masked CMB maps
to high accuracy. We propose an innovative neural network architecture, the
WienerNet, which guarantees linearity in the data map. Our method does not
require Wiener filtered training data, but rather learns Wiener filtering from
tailored loss functions which are mathematically guaranteed to be minimized by
the exact solution. Once trained, the neural network Wiener filter is extremely
fast, about a factor of 1000 faster than the standard conjugate gradient
method. Wiener filtering is the computational bottleneck in many optimal CMB
analyses, including power spectrum estimation, lensing and non-Gaussianities,
and our method could potentially be used to speed them up by orders of
magnitude with minimal loss of optimality. The method should also be useful to
analyze other statistical fields in cosmology.
