Learning from deep learning: better cosmological parameter inference from weak lensing maps

Dark matter cannot be observed directly, but its weak gravitational lensing slightly distorts the apparent shapes of background galaxies, making weak lensing one of the most promising probes of cosmology. Several observational studies have measured the effect, and there are currently running1,2 and planned efforts3,4 to provide even larger and higher-resolution weak lensing maps. Owing to nonlinearities on small scales, the traditional analysis with two-point statistics does not fully capture all of the underlying information5. Multiple inference methods have been proposed to extract more details based on higher-order statistics6,7, peak statistics8–13, Minkowski functionals14–16 and recently convolutional neural networks17,18. Here we present an improved convolutional neural network that gives significantly better estimates of the Ωm and σ8 cosmological parameters from simulated weak lensing convergence maps than state-of-art methods and that is also free of systematic bias. We show that the network exploits information in the gradients around peaks, and with this insight we have constructed an easy-to-understand and robust peak-counting algorithm based on the steepness of peaks, instead of their heights. The proposed scheme is even more accurate than the neural network on high-resolution noiseless maps. With shape noise and lower resolution, its relative advantage deteriorates, but it remains more accurate than peak counting.A convolutional neural network estimates cosmological parameters from simulated weak lensing convergence maps in an unbiased way. The network analysis motivates a new and robust convergence peak-counting algorithm based on the steepness of peak heights.