Astrophysics and cosmology with the scattering transform

Quantifying textures and patterns in physical data is an important but challenging task. Recently, a novel statistic borrowing ideas from convolutional neural networks (CNNs), called the scattering transform, has shown its great potential. It is a sweet spot between the power spectrum and CNNs: it yields a compact set of summary statistics with a simple definition while sharing the high performance of CNNs. In this thesis, I provide intuitive understandings and interpretations for the scattering transform. I also discuss its connection to and advantages over other common statistics such as the N-point functions. I argue that its informativeness, robustness, compactness, and interpretability make it an ideal statistic for practical data analysis of fields with complex structures. Then, I show promising examples of its applications in physics research, including rigid parameter inference tasks in cosmology, where it has a performance on a par with CNNs and exploratory data analyses in astronomy and oceanography

A new approach to observational cosmology using the scattering transform

Parameter estimation with non-Gaussian stochastic fields is a common challenge in astrophysics and cosmology. In this paper we advocate performing this task using the scattering transform, a statistical tool rooted in the mathematical properties of convolutional neural nets. This estimator can characterize a complex field without explicitly computing higher-order statistics, thus avoiding the high variance and dimensionality problems. It generates a compact set of coefficients which can be used as robust summary statistics for non-Gaussian information. It is especially suited for fields presenting localized structures and hierarchical clustering, such as the cosmological density field. To demonstrate its power, we apply this estimator to the cosmological parameter inference problem in the context of weak lensing. Using simulated convergence maps with realistic noise, the scattering transform outperforms the power spectrum and peak counts, and is on par with the state-of-the-art CNN. It retains the advantages of traditional statistical descriptors (it does not require any training nor tuning), has provable stability properties, allows to check for systematics, and importantly, the scattering coefficients are interpretable. It is a powerful and attractive estimator for observational cosmology and, in general, the study of physically-motivated fields.Comment: 15 pages, 7 figures; comments welcom