Creating Virtual Universes Using Generative Adversarial Networks

Inferring model parameters from experimental data is a grand challenge in many sciences, including cosmology. This often relies critically on high fidelity numerical simulations, which are prohibitively computationally expensive. The application of deep learning techniques to generative modeling is renewing interest in using high dimensional density estimators as computationally inexpensive emulators of fully-fledged simulations. These generative models have the potential to make a dramatic shift in the field of scientific simulations, but for that shift to happen we need to study the performance of such generators in the precision regime needed for science applications. To this end, in this letter we apply Generative Adversarial Networks to the problem of generating cosmological weak lensing convergence maps. We show that our generator network produces maps that are described by, with high statistical confidence, the same summary statistics as the fully simulated maps. The scientific success of the next generation of sky surveys (e.g. [1–5]) to test the current “standard model” of cosmology (ΛCDM), hinges critically on the success of underlying simulations. Answering questions in cosmology about the nature of cold dark matter, dark energy and the inflation of the early universe, requires relating observations of a large number of astrophysical objects which trace the underlying matter density field, to simulations of “virtual universes” with different cosmological parameters. Currently the creation of each virtual universe requires an extremely computationally expensive simulation on High Performance Computing resources. In order to make this inverse problem practically solvable, constructing a computationally cheap surrogate model or an emulator [6, 7] is imperative. However, traditional approaches to emulators require the use of a summary-statistic which is to be emulated. An approach that does not require such mathematical templates of the simulation outcome would be of considerable value in the field. The ability to emulate these simulations with high fidelity, in a fraction of the computational time, would boost our ability to understand the fundamental nature of the universe. While in this letter we focus our attention on cosmology, and in particular weak lensing convergence maps, we believe that this approach is relevant to many areas of science and engineering. Recent developments in deep generative modeling techniques open the potential to meet this need. The density estimators in these models are built out of neural networks which can serve as universal approximators [8], thus having the ability to learn the underlying distributions of data and emulate the observable without being biased by the choice of summary-statistics, ∗Corresponding author: mmustafa@lbl.gov as in the traditional approach to emulators. In this letter, we study the ability of a recent variant of generative models Generative Adversarial Networks (GANs) [9] to generate weak lensing convergence maps. The training and validation maps are produced using N-body simulations of ΛCDM cosmology. We show that maps generated by the neural network exhibit, with high statistical confidence, the same power (Fourier) spectrum of the fully-fledged simulator maps, as well as higher order non-Gaussian features, thus demonstrating that such scientific data is amenable to a GAN treatment for generation. The very high level of agreement we achieve offers promise for building emulators out of deep neural networks. We first present our results and analysis then outline the future investigations which we think are critical to build such emulators in the Discussion section.