Planck Limits on Cosmic String Tension Using Machine Learning

We develop two parallel machine-learning pipelines to estimate the contribution of cosmic strings (CSs), conveniently encoded in their tension ($G\mu$), to the anisotropies of the cosmic microwave background radiation observed by {\it Planck}. The first approach is tree-based and feeds on certain map features derived by image processing and statistical tools. The second uses convolutional neural network with the goal to explore possible non-trivial features of the CS imprints. The two pipelines are trained on {\it Planck} simulations and when applied to {\it Planck}\texttt{SMICA} map yield the $3\sigma$ upper bound of $G\mu\lesssim 8.6\times 10^{-7}$. We also train and apply the pipelines to make forecasts for futuristic CMB-S4-like surveys and conservatively find their minimum detectable tension to be $G\mu_{\rm min}\sim 1.9\times 10^{-7}$.