Deep Learning for Observational Cosmology
We capitalise on the latest developments in the field of Deep Convolutional Neural Networks (CNN) and Generative Adversarial Networks (GAN) for solving some of the most important problems in the field of Observational Cosmology. The advantage of neural networks over classical statistical methods that are currently used in cosmology is that they are able to learn complex nonlinear relations present in the cosmological data. Applications of deep learning techniques have the potential to radically improve on existing data analysis methods in several areas of cosmology and astrophysics. In this proposed project, we plan to tackle three specific problems:
- improving the precision of measurement of cosmological parameters from dark matter maps using CNNs
- generating cosmological N-body simulations using generative machine learning techniques
- creating deep learning algorithms to operate on the sphere.
Read the article about this project on our blog:
Deepsphere: a Neural Network Architecture for Spherical Data
The main goal of this project is to capitalise on the latest developments in the field of Deep Convolutional Neural Networks (CNN) and Generative Adversarial Networks (GAN) for solving some of the most important problems in the field of Observational Cosmology. The advantage of neural networks over classical statistical methods that are currently used in cosmology is that they are able to learn complex nonlinear relations from the data. Applications of deep learning techniques have the potential to radically improve on existing data analysis methods in several areas of cosmology and astrophysics. In this proposed project, we plan to tackle three specific problems:
- At present the standard statistical measure in weak lensing, and most areas of cosmology, is the power spectrum. For gaussian random fields, it is known that this statistic captures all the available information. However, the fields that we measure in cosmology can be highly non-gaussian making the power spectrum measure suboptimal. We plan to develop a CNN-based method that will allow us to fully capture the non-gaussian features of cosmological data, which will allow us to make more precise measurements.
- Making theoretical predictions for the expected non-gaussian signals in cosmology currently requires extensive numerical simulations that are computationally expensive. In this part of the project we plan to use a GAN which will be trained on cosmological simulations to generate new instances of the cosmic web. This will have the advantage of being extremely fast compared to current existing methods. These fast simulations can be used in tandem with full physical numerical simulations to create a model of cosmological observables and uncertainties, both faster and more accurately.
- Developing algorithms to perform convolutional neural network analysis on the sphere, in the Healpix sampling scheme, which is most commonly used in cosmology. To date, the CNN-based analysis used only 2D image-like data. As the data available for these measurements will soon cover a significant part of the sky, the need of performing the analysis on the sphere will become pressing.
Solving these three problems benefits the machine learning community in several ways. For example, very few quantitative tests of the performance of GANs have been done to date in the field of machine learning. As the application to cosmological data would involve stringent quantitative testing, this project would allow for better evaluations of generative models. Another challenge that will push the limit of existing machine learning techniques is the need for processing large three-dimensional cosmological data. Most existing deep learning methods work on 2-dimensional data and although the extension to 3-dimensional data is straightforward, it nevertheless comes with additional constraints on the amount of memory required, especially when using GPUs. We here would like to exploit advanced analytic solutions to reduce the memory footprint of neural networks for 3-dimensional data. The development of such solutions is likely to benefit other scientific fields that have similar types of data to analyse, including the medical domain or material science.
An important part of the technology development process is taking a prototype algorithm and transforming it into a production-ready framework, which can benefit the community. A number of data science challenges will be present in that process, which would be very hard to address without the SDSC expertise. Such challenges may include: making the models work on 3- or higher- dimensional data, scaling the problem to use higher resolution images, building a platform for efficient training of the methods for multiple cosmological models, optimising network architectures and training strategies (optimisation engines, regularisation), creating a framework where experiments can be efficiently and systematically repeated to assure the quantitative accuracy of the methods, such that they meet the science requirements and can benefit the community of users.
Fig. 1: Comparison between the precision of measurement from the commonly-used power spectrum and the deep convolutional neural network. The contours signify 95% and 68% confidence intervals. From Fluri et al. 2018.
Fig. 2: Slice through a 3D dark matter simulation cube. Left: the real simulation at high resolution, middle: the real simulation at low resolution, right: high resolution draw from a GAN corresponding to the low resolution input. From Perraudin et al 2019.
Fig. 3: Architecture of a spherical convolutional neural network utilising graph networks. From Perraudin et al. 2019.
Fluri, J; Kacprzak, T; Réfrégier, A; Amara, A; Lucchi, A; Hofmann, T; “Cosmological constraints from noisy convergence maps through deep learning”, Physical Review D, Volume 98, id123518 link
Fluri, J; Kacprzak, T; Lucchi, A; Refregier, A; Amara, A; Hofmann, T; Schneider, A; “Cosmological constraints with deep learning from KiDS-450 weak lensing maps”, Physical Review D, Volume 100, id063514 link
Perraudin, N; Defferrard, M; Kacprzak, T; Sgier, R; “DeepSphere: Efficient spherical convolutional neural network with HEALPix sampling for cosmological applications”, Astronomy and Computing, Volume 27, April 2019, Pages 130-146 link
Perraudin, N; Srivastava, A; Lucchi, A; Kacprzak, T; Hofmann, T; Réfrégier, A; “Cosmological N-body simulations: a challenge for scalable generative models”, Computational Astrophysics and Cosmology (Springer Open), Volume 6, Article number: 5 (2019) link
Perraudin, N; Marcon, S; Lucchi, A; Kacprzak, T; “Emulation of cosmological mass maps with conditional generative adversarial networks”, Frontiers in Artificial Intelligence, 04 June 2021, link
3D wGAN sequence for N-body cube generation, progressively increasing the resolution:
GitHub – nperraud/3DcosmoGAN
2D conditional wGAN for cosmological mass maps:
Nathanaël Perraudin / DarkMatterGAN
Using graph neural networks for deep learning on the sphere with Healpix sampling
GitHub – deepsphere/deepsphere-cosmo-tf1: A spherical convolutional neural network for cosmology (TFv1).
Public dataset for spherical mass maps (Zenodo):
Spherical convergence maps dataset
Workshop AICosmo2019 in Ascona (organisers: Tomasz Kacprzak, Aurelien Lucchi, Nathanaël Perraudin)
Artificial Intelligence methods in Cosmology Ascona 9-12 June 2019