Convolutional Neural Networks (CNN) have recently been demonstrated on synthetic data to improve upon the precision of cosmological inference. In particular they have the potential to yield more precise cosmological constraints from weak lensing mass maps than the two-point functions. We present the cosmological results with a CNN from the KiDS-450 tomographic weak lensing dataset, constraining the total matter density Ωm, the fluctuation amplitude σ8, and the intrinsic alignment amplitude AIA. We use a grid of N-body simulations to generate a training set of tomographic weak lensing maps. We test the robustness of the expected constraints to various effects, such as baryonic feedback, simulation accuracy, different value of H0, or the lightcone projection technique. We train a set of ResNet-based CNNs with varying depths to analyze sets of tomographic KiDS mass maps divided into 20 flat regions, with applied Gaussian smoothing of σ = 2.34 arcmin. The uncertainties on shear calibration and n(z) error are marginalized in the likelihood pipeline. Following a blinding scheme, we derive constraints of S8 = σ8(Ωm/0.3) 0.5 = 0.777 +0.038 −0.036 with our CNN analysis, with AIA = 1.398 +0.779 −0.724 . We compare this result to the power spectrum analysis on the same maps and likelihood pipeline and find an improvement of about 30% for the CNN. We discuss how our results offer excellent prospects for the use of deep learning in future cosmological data analysis.

Cosmic shear data contains a large amount of cosmological information encapsulated in the non-Gaussian features of the weak lensing mass maps. Weak lensing studies mostly rely on two-point statistics to constrain cosmology from cosmic shear data, that do not capture all of this information. Additional non-Gaussian information can be extracted using non-Gaussian statistics. We compare the constraining power in the Ωm–σ8 plane of three map-based non-Gaussian statistics with the angular power spectrum, namely; peak counts, minimum counts and Minkowski functionals. We further analyze the impact of tomography and systematic effects originating from galaxy intrinsic alignments, multiplicative shear bias and photometric redshift systematics. We forecast the performance of the statistics for a stage-3-like weak lensing survey, spanning an area of 5000 deg2 and restrict ourselves to scales ⩾ 10 arcmin to avoid baryonic effects. The study follows a forward modelling scheme to predict the statistics at different cosmologies based on N-Body simulations. We find, that in our setup, the considered non-Gaussian statistics provide tighter constraints than the angular power spectrum. The peak counts show the greatest potential, increasing the figure-of-Merit (FoM) in the Ωm–σ8 plane by a factor of about 6, while the minimum counts and the Minkowski functionals yield an increase by a factor of about 3 and 2, respectively. A combined analysis using all non-Gaussian statistics in addition to the power spectrum increases the FoM by a factor of 9 and reduces the error on S8 by ≈ 30%. We find that the importance of tomography is diminished when combining non-Gaussian statistics with the angular power spectrum. The non-Gaussian statistics indeed profit less from tomography and the minimum counts and Minkowski functionals add some robustness against galaxy intrinsic alignment in a non-tomographic setting. We further find that a combination of the angular power spectrum and the non-Gaussian statistics allows us to apply conservative scale cuts in the analysis, thus helping to minimize the impact of baryonic and relativistic effects, while conserving the cosmological constraining power. We make the code that was used to conduct this analysis publicly available to simplify performing such analyses in the future.

Dark matter in the universe evolves through gravity to form a complex network of halos, filaments, sheets and voids, that is known as the cosmic web. Computational models of the underlying physical processes, such as classical N-body simulations, are extremely resource intensive, as they track the action of gravity in an expanding universe using billions of particles as tracers of the cosmic matter distribution. Therefore, upcoming cosmology experiments will face a computational bottleneck that may limit the exploitation of their full scientific potential. To address this challenge, we demonstrate the application of a machine learning technique called Generative Adversarial Networks (GAN) to learn models that can efficiently generate new, physically realistic realizations of the cosmic web. Our training set is a small, representative sample of 2D image snapshots from N-body simulations of size 500 and 100 Mpc. We show that the GAN-generated samples are qualitatively and quantitatively very similar to the originals. For the larger boxes of size 500 Mpc, it is very difficult to distinguish them visually. The agreement of the power spectrum P k is 1-2% for most of the range, between k = 0.06 and k = 0.4. For the remaining values of k, the agreement is within 15%, with the error rate increasing for k > 0.8. For smaller boxes of size 100 Mpc, we find that the visual agreement to be good, but some differences are noticable. The error on the power spectrum is of the order of 20%. We attribute this loss of performance to the fact that the matter distribution in 100 Mpc cutouts was very inhomogeneous between images, a situation in which the performance of GANs is known to deteriorate. We find a good match for the correlation matrix of full P k range for 100 Mpc data and of small scales for 500 Mpc, with ∼20% disagreement for large scales. An important advantage of generating cosmic web realizations with a GAN is the considerable gains in terms of computation time. Each new sample generated by a GAN takes a fraction of a second, compared to the many hours needed by traditional N-body techniques. We anticipate that the use of generative models such as GANs will therefore play an important role in providing extremely fast and precise simulations of cosmic web in the era of large cosmological surveys, such as Euclid and Large Synoptic Survey Telescope (LSST).

Deep learning is a powerful analysis technique that has recently been proposed as a method to constrain cosmological parameters from weak lensing mass maps. Due to its ability to learn relevant features from the data, it is able to extract more information from the mass maps than the commonly used power spectrum, and thus achieve better precision for cosmological parameter measurement. We explore the advantage of Convolutional Neural Networks (CNN) over the power spectrum for varying levels of shape noise and different smoothing scales applied to the maps. We compare the cosmological constraints from the two methods in the ΩM −σ8 plane for sets of 400 deg 2 convergence maps. We find that, for a shape noise level corresponding to 8.53 galaxies/arcmin 2 and the smoothing scale of σs = 2.34 arcmin, the network is able to generate 45% tighter constraints. For smaller smoothing scale of σs = 1.17 the improvement can reach ∼ 50%, while for larger smoothing scale of σs = 5.85, the improvement decreases to 19%. The advantage generally decreases when the noise level and smoothing scales increase. We present a new training strategy to train the neural network with noisy data, as well as considerations for practical applications of the deep learning approach.arXiv:1807.08732v2 [astro-ph.CO]

We constrain the matter density Ωm and the amplitude of density fluctuations σ8 within the ΛCDM cosmological model with shear peak statistics and angular convergence power spectra using mass maps constructed from the first three years of data of the Dark Energy Survey (DES Y3). We use tomographic shear peak statistics, including cross-peaks: peak counts calculated on maps created by taking a harmonic space product of the convergence of two tomographic redshift bins. Our analysis follows a forward-modelling scheme to create a likelihood of these statistics using N-body simulations, using a Gaussian process emulator. We take into account the uncertainty from the remaining, largely unconstrained ΛCDM parameters (Ωb, ns and h). We include the following lensing systematics: multiplicative shear bias, photometric redshift uncertainty, and galaxy intrinsic alignment. Stringent scale cuts are applied to avoid biases from unmodelled baryonic physics. We find that the additional non-Gaussian information leads to a tightening of the constraints on the structure growth parameter yielding $S_8~\equiv ~\sigma _8\sqrt{\Omega _{\mathrm{m}}/0.3}~=~0.797_{-0.013}^{+0.015}$ (68 per cent confidence limits), with a precision of 1.8 per cent, an improvement of  38 per cent compared to the angular power spectra only case. The results obtained with the angular power spectra and peak counts are found to be in agreement with each other and no significant difference in S8 is recorded. We find a mild tension of 1.5 σ between our study and the results from Planck 2018, with our analysis yielding a lower S8. Furthermore, we observe that the combination of angular power spectra and tomographic peak counts breaks the degeneracy between galaxy intrinsic alignment AIA and S8, improving cosmological constraints. We run a suite of tests concluding that our results are robust and consistent with the results from other studies using DES Y3 data.