[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-128348-en":3,"doc-seo-128348-105":31,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},128348,962085564549,"Genevieve","https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45",8,"Research & Report","Weak Gravitational Lensing Cosmology with Novel Analytical and Machine Learning Frameworks","Modern cosmology requires robust analysis of the large data sets produced by weak gravitational lensing surveys. This dissertation develops statistical tools from both analytical theory and machine-learning perspectives to improve understanding of cosmological models and structure formation. Analytically, it derives power spectra and two-point correlations of weak-lensing critical points in mildly non-Gaussian convergence fields and models their clustering via bias expansion up to NNLO as a benchmark for N-body simulations. For survey data, it builds a likelihood-analysis pipeline using the integrated shear 3-point correlation function ζ± and a high-precision neural-emulator framework for fast MCMC parameter inference, improving constraints on key parameters.","Weak Gravitational Lensing Cosmology with Novel Analytical and Machine Learning Frameworks  \nZhengyangguang Gong  \nM¨unchen 2025  \nWeak Gravitational Lensing Cosmology with Novel Analytical and Machine Learning Frameworks  \nZhengyangguang Gong  \nDissertation an der Fakult¨at f¨ur Physik der Ludwig–Maximilians–Universit¨at M¨unchen  \nvorgelegt von Zhengyangguang Gong aus Hefei, China  \nM¨unchen, den 15.05.2025  \nErstgutachter: Prof. Dr. Ralf Bender  \nZweitgutachter: Prof. Dr. Eiichiro Komatsu Tag der m¨undlichen Pr¨ufung: 15.07.2025  \nContents  \nZusammenfassung vii  \nAbstract ix  \n1 Introduction to cosmology 1  \n1.1 Foundations of the cosmological dynamics .................. 2  \n1.2 Cosmological distance measurement ...................... 6  \n1.3 Standard ΛCDM parametrization ....................... 7  \n1.4 Cosmological experiments ........................... 9  \n2 Statistics and perturbation theory of cosmic density fields 15  \n2.1 Random fields .................................. 16  \n2.1.1 Homogeneity, isotropy and ergodicity ................. 16  \n2.1.2 PDF, moments and cumulants ..................... 17  \n2.2 Density perturbation and its correlation functions .............. 19  \n2.2.1 Power spectrum ............................. 21  \n2.2.2 Gravitational dynamics of the density perturbation field ...... 23  \n2.2.3 Standard perturbation theory ..................... 24  \n2.3 Weak lensing cosmology ............................ 27  \n2.3.1 Weak lensing basics ........................... 27  \n2.3.2 Weak lensing measurement ....................... 29  \n2.3.3 Weak lensing shear 2PCF and integrated 3PCF ........... 32  \n2.4 Bias theory in large-scale structure ...................... 34  \n2.4.1 Galaxy bias ............................... 34  \n2.4.2 Extrema bias in weak lensing field ................... 36  \n2.5 Statistical analysis with multiprobe cosmology ................ 39  \n3 Basic machine learning concepts and their applications to cosmology 41  \n3.1 Multilayer perceptron (MLP) ......................... 42  \n3.1.1 Training, validation, optimization and testing ............ 42  \n3.1.2 Emulators for the shear integrated 3PCF ............... 44  \n3.2 Convolutional neural network (CNN) ..................... 46  \n3.2.1 Fundamental principles of CNNs ................... 46  \n3.2.2 Interpretable C3NN ........................... 48  \n3.3 Simulation-based inference (SBI) ....................... 49  \n3.3.1 SBI with C3NN ............................. 51  \n4 Intermezzo: integrating analytical methods and machine learning in cosmology 55  \n5 Clustering of the extreme: A theoretical description of weak lensing  \ncritical points power spectra in the mildly nonlinear regime 59  \n6 Cosmology from the integrated shear 3-point correlation function: sim  \nulated likelihood analyses with machine-learning emulators 89  \n7 C3NN: Cosmological Correlator Convolutional Neural Network an Inter  \npretable Machine-learning Framework for Cosmological Analyses 123  \n8 Making the leap. Part I. Modelling the reconstructed lensing conver  \ngence PDF from cosmic shear with survey masks and systematics 141  \n9 Summary and conclusions 183  \nAcknowledgments 194  \nZusammenfassung  \nModerne kosmologische Experimente wie Euclid, Vera Rubin LSST und DESI werden enorme Datenmengen liefern, deren Analyse eine zentrale Herausforderung darstellt. Maschinelles Lernen (ML) hat sich in Bereichen wie Systemklassifikation, synthetische Datengenerierung und Parameterinferenz etabliert und hat erheblich zur Datenanalyse beigetragen. Dennoch bestehen Bedenken hinsichtlich Genauigkeit, Robustheit und Interpretierbarkeit von ML-Ans¨atzen. Zudem bleibt die Kombination analytischer Methoden mit ML-Techniken weitgehend unerforscht.  \nIn dieser Arbeit werden statistische Analysemethoden f¨ur schwache Gravitationslinsenfelder sowohl aus analytischer als auch aus maschineller Lernperspektive entwickelt, mit dem Ziel, unser Verst¨andnis von kosmologischen Modellen, Strukturbildung und Entwi","cbCainiRRufFe6X2","https://ap.wps.com/l/cbCainiRRufFe6X2","pdf",10274102,3,1,206,"English","en",105,"# Contents\n## 1 Introduction to cosmology\n## 2 Statistics and perturbation theory of cosmic density fields\n## 3 Basic machine learning concepts and their applications to cosmology\n## 4 Intermezzo: integrating analytical methods and machine learning in cosmology\n## 5 Clustering of the extreme\n## 6 Cosmology from the integrated shear 3-point correlation function\n## 7 C3NN: Cosmological Correlator Convolutional Neural Network\n## 8 Making the leap. Part I\n## 9 Summary and conclusions","[{\"question\":\"What analytical results does the dissertation provide for weak lensing fields?\",\"answer\":\"It derives explicit formulas for power spectra and two-point correlation functions of 2D weak-lensing critical points, covering peaks, voids, and saddle points, including clustering modeling via a perturbative bias expansion up to NNLO.\"},{\"question\":\"How does the work use machine learning in cosmological inference?\",\"answer\":\"It develops a likelihood-analysis pipeline based on the integrated shear 3-point correlation function ζ± and uses a high-precision neural-network emulator to enable fast theoretical predictions within MCMC parameter inference.\"},{\"question\":\"Why is interpretability emphasized, and what framework addresses it?\",\"answer\":\"Interpretability is targeted by introducing the Cosmological Correlator Convolutional Neural Network (C3NN), a hybrid approach that combines convolutional neural networks with cosmological N-point correlation functions to connect ML outputs with known statistical structures.\"}]","Weak Gravitational Lensing Cosmology with Novel Analytical and Machine Learning Frameworks | 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