Weak gravitational lensing cosmology with novel analytical and machine learning frameworks

Gong, Zhengyangguang (2025): Weak gravitational lensing cosmology with novel analytical and machine learning frameworks. Dissertation, LMU München: Faculty of Physics

Abstract

Modern cosmological experiments such as Euclid, Vera Rubin’s LSST, and the Dark Energy Spectroscopic Instrument (DESI) will generate an unprecedented volume of data in the coming years. Effectively analyzing this vast dataset to deepen our understanding of the Universe is an urgent challenge. In response, machine learning (ML) techniques have emerged across various areas of cosmological research, including image classification, synthetic data generation, and parameter inference, significantly enhanced real data analyses. However, concerns remain about the accuracy, robustness, and interpretability of ML approaches. Furthermore, the integration of conventional analytical methods with cutting-edge ML techniques is an underexplored avenue. This thesis develops statistical analysis methods for weak gravitational lensing fields from both analytical and machine learning perspectives, aiming to improve our understanding of cosmological models, structure formation, and evolution. On the analytical side, I derive explicit formulae for the power spectra and two-point correlation functions (2PCFs) of 2D critical points, including peaks (maxima), voids (minima), and saddle points, in weak gravitational lensing convergence field with mild non-Gaussianity. Using a perturbative bias expansion, I model their clustering and derive the power spectrum of weak lensing critical points up to next-to-next-to-leading order (NNLO), incorporating trispectrum configurations. This serves as a benchmark test for N-body simulations, ensuring that statistics such as lensing peak and void clustering are not biased by simulation systematics. For the ML application to survey data analysis, I collaborated on the development of a likelihood analysis pipeline for cosmological constraints using the integrated shear three-point correlation function ζ ± . Specifically, I built a high-precision neural network emulator for fast theoretical predictions in parameter inference using Markov Chain Monte Carlo (MCMC). With simulated data that mimics the Dark Energy Survey (DES) Year-3 footprint, mask, and source tomographic bins, we demonstrate that incorporating ζ ± alongside the conventional shear 2PCF ξ ± improves constraints on key cosmological parameters, such as As (or σ8) and w0, by approximately 10 − 25%. To address the challenge of ML interpretability and better integrate it with analytical approaches, I introduce the Cosmological Correlator Convolutional Neural Network (C3NN), a hybrid framework that merges convolutional neural networks (CNNs) with cosmological N-point correlation functions (NPCFs). We show that the C3NN output can be explicitly expressed in terms of analytically tractable NPCFs, allowing us to open the “black box” of ML. Along with auxiliary algorithms, this approach enables a quantitative ranking of different orders of NPCF based on their contribution to classification tasks, providing deeper insights from the learned features into cosmological physics.

Abstract

Abstract

• Item Type: Theses (Dissertation, LMU Munich)
• Keywords: Cosmology, Weak gravitational lensing, Large-scale structure, Machine learning, information beyond Gaussianity
• Subjects: 500 Natural sciences and mathematics; 500 Natural sciences and mathematics > 530 Physics
• Faculties: Faculty of Physics
• Language: English
• Date of oral examination: 15. July 2025
• 1. Referee: Bender, Ralf
• Signature of the printed copy: 0001/UMC 31403