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:

1. 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.
2. 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.
3. 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.