Non-Gaussian information from weak lensing data via deep learning

Weak lensing maps contain information beyond two-point statistics on small scales. Much recent work has tried to extract this information through a range of different observables or via nonlinear transformations of the lensing field. Here we train and apply a two-dimensional convolutional neural network to simulated noiseless lensing maps covering 96 different cosmological models over a range of ${{\mathrm{\ensuremath{\Omega}}}_{m},{\ensuremath{\sigma}}_{8}}$. Using the area of the confidence contour in the ${{\mathrm{\ensuremath{\Omega}}}_{m},{\ensuremath{\sigma}}_{8}}$ plane as a figure of merit, derived from simulated convergence maps smoothed on a scale of 1.0 arcmin, we show that the neural network yields $\ensuremath{\approx}5\ifmmode\times\else\texttimes\fi{}$ tighter constraints than the power spectrum, and $\ensuremath{\approx}4\ifmmode\times\else\texttimes\fi{}$ tighter than the lensing peaks. Such gains illustrate the extent to which weak lensing data encode cosmological information not accessible to the power spectrum or even other, non-Gaussian statistics such as lensing peaks.