Fast Wiener filtering with neural networks
We developed a method to perform Wiener Filtering of Gaussian fields with an innovative neural network approach. Wiener filtering (or inverse covariance filtering) is the computational bottleneck of optimal analyses of near-Gaussian random fields, which are ubiquitous in cosmology. Our neural network, after training, is able to Wiener filter CMB maps a thousand times faster than the standard conjugate gradient method, with minimal loss of optimality. Our network architecture, the WienerNet, is linear in the CMB data (but depends non-linearly on the noise), unlike ordinary neural networks, so it is guaranteed to preserve Gaussianity. The network combines recent insights from the machine learning community with analytic knowledge from physics. We show how a physically motivated loss function outperforms naïve supervised learning significantly. Our paper has shown an exciting way forward in combining machine learning with classical data analysis, as well as bringing physical knowledge into machine learning algorithms and was accepted to the NeurIPS conference on machine learning.