An improved cosmological parameter inference scheme motivated by deep learning

Abstract

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 running [1,2], and planned efforts [3,4] to provide even larger, and higher resolution weak lensing maps. Due to nonlinearities on small scales, the traditional analysis with two-point statistics does not fully capture all the underlying information [5]. Multiple inference methods were proposed to extract more details based on higher order statistics [6, 7], peak statistics [8][9][10][11][12][13], Minkowski functionals [14-16] and recently convolutional neural networks (CNN) [17,18]. Here we present an improved convolutional neural network that gives significantly better estimates of Ω m and σ 8 cosmological parameters from simulated convergence maps than the state of art methods and also is free of systematic bias. We show that the network exploits information in the gradients around peaks, and with this insight, we construct a new, 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.Following the idea and using the simulation data from a recent study [18] we created an improved convolutional neural network (CNN) architecture (see details in the Methods) which is able to recover cosmological parameters more accurately from simulated weak lensing maps. The input of the network is a set of mock convergence (κ) maps generated by ray-tracing n-body simulations with 96 different values for the matter density Ω m and the scale of the initial perturbations normalized at the late Universe, σ 8 (see [18] and [19] for details of the weak lensing map generation), the outputs of the network were the predicted cosmological parameters. The modifications of the CNN mostly consisted of adding further activations, increasing the number of filters, and introducing a regular block structure, following successful computer vision models [20,21].

Deep learning for a space-variant deconvolution in galaxy surveys

“…The first features learned in convolutive deep neural networks typically correspond to edges at particular orientation and location in the images (LeCun et al 2015), which is also what the wavelet transforms extract at different scales. Similar observations were noted for features learned with a CNN in the context of cosmological parameter estimations from weak-lensing convergence maps (Ribli et al 2019). Understanding mathematically how the architecture of such networks captures progressively powerful invariants can also be approached through wavelets and their use in the wavelet-scattering transform (Mallat 2016).…”

Dark Energy Survey Year 3 results: Curved-sky weak lensing mass map reconstruction

“…non-Gaussian) summary statistics, and whether we understand, at the same level as the two-point statistics, the non-trivial systematic effects in these higher-order statistics. Common higher-order statistics with weak lensing include shear peak statistics (Dietrich & Hartlap 2010;Kratochvil et al 2010;Liu et al 2015;Kacprzak et al 2016;Martinet et al 2018;Peel et al 2018;Shan et al 2018;Ajani et al 2020), higher moments of the weak lensing convergence (Van Waerbeke et al 2013;Petri et al 2015;Vicinanza et al 2016;Chang et al 2018;Vicinanza et al 2018;Peel et al 2018;Gatti et al 2020b), three-point correlation functions or bispectra (Takada & Jain 2003Semboloni et al 2011;Fu et al 2014), Minkowski functionals (Kratochvil et al 2012;Petri et al 2015;Vicinanza et al 2019;Parroni et al 2020), and machine-learning methods (Ribli et al 2019;Fluri et al 2018Fluri et al , 2019Jeffrey et al 2021). Many of these have recently been applied to data (Liu et al 2015;Kacprzak et al 2016;Martinet et al 2018;Fluri et al 2019;Jeffrey et al 2021), often performing well in terms of cosmological constraints.…”

Galaxy shape measurement with convolutional neural networks

“…Further tests with CNN shape estimators in simulations could improve our understanding of factors which contribute to the performance advantage of the CNN compared to a maximum likelihood model fitting approach. The extraction of meaningful and interpretable knowledge from the inspection of a CNN could also improve our understanding of the problem itself (Ribli et al 2019b). Finally, in our proposed scheme, galaxy shape estimation with CNNs cannot completely replace model fitting approaches, as the training procedure relies on high-quality shape measurements from a deeper survey which must be performed with conventional methods.…”