Application of information geometry methods in the development of nuclear structure models

doctoral thesis

• Title (croatian): Primjena metoda informacijske geometrije u razvoju modela nuklearne strukture
• Author: Marko Imbrišak
• Mentor: Kosuke Nomura (mentor)
• Committee member: Tamara Nikšić (predsjednik povjerenstva)
• Committee member: Nils Paar (član povjerenstva)
• Committee member: Tea Mijatović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2023-07-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics
• Universal decimal classification (UDC): 53 - Physics

Abstract

Statistical analysis proved to be significant in determining the errors of theoretical models, assessing the risk of extrapolation and the sensitivity of the model to changes, as well as in the description of instabilities in the models. However, the importance of applying the analysis of the unreliability of individual parameters in the form of nuclear energy density functionals has only recently been recognized, where one of the main problems of error analysis of the parameters of those models is the possible sloppiness of some parameters or their combinations. This was precisely the motivation for using methods of reducing the number of model parameters based on information geometry - an interdisciplinary field that applies the ideas of differential geometry to statistical problems that have recently found application in the physical description of various systems in physics, chemistry and biology. Since in nuclear physics the manifold boundary approximation method (MBAM) has recently proved useful for the classification and reduction of complex models such as EDF models of the atomic nucleus, the statistical nature of determining the unreliability by the MBAM method was investigated in more detail using the example of the DD-PC1 functional. Also, using automatic differentiation in the code of the DD-PC1 functional and the MBAM method, a more thorough and precise analysis of the unreliability of the parameters itself is obtained, which enabled the optimization of time and numerical precision. Considering the novelty of the MBAM method itself, stability tests of the conclusions obtained by MBAM geodesics based on differential geometry techniques in the field of classical statistics and Bayesian statistics in the form of the Markov Chain Monte Carlo method were conducted.

Abstract (croatian)

Statistička analiza pokazala se značajna pri određivanju pogrešaka teorijskih modela, procjeni rizika ekstrapolacije i osjetljivosti modela na promjene kao i pri opisu nestabilnosti u modelima. Međutim, tek je nedavno prepoznat značaj primjene analize nepouzdanosti parametera nuklearnih energijskih funkcionala gustoće. Jedan od glavnih problema analize pogrešaka parametara tih modela moguća je aljkavost nekih parametara ili njihovih kombinacija. Upravo je to bila motivacija za korištenje metoda redukcije broja parametara modela temeljenih na informacijskoj geometriji - interdisciplinarnom području koje primjenjuje ideje diferencijalne geometrije na statističke probleme koje je odnedavno našlo primjenu u fizikalnom opisu različitih sustava u fizici, kemiji i biologiji. Budući da se u nuklearnoj fizici metoda aproksimacije modela mnogostrukosti s rubom (MBAM) nedavno pokazala korisnom za klasifikaciju i redukciju kompleksnih modela kao što su EDF modeli atomske jezgre, podrobnije je istražena statistička priroda određivanja nepouzdanosti MBAM metodom na primjeru DD-PC1 funkcionala. Također, koristeći automatsku diferencijaciju u kodu DD-PC1 funkcionala te MBAM metode, dobiva se temeljitija i preciznija analiza nepouzdanosti samih parametara čime se omogućila optimizacija vremena i numeričke preciznosti. S obzirom na novost same MBAM metode, provedeni su testovi stabilnosti zaključaka dobivenih MBAM geodezicima temeljeni na tehnikama diferencijalne geometrije u području klasične statistike te Bayesove statistike u vidu Markov Chain Monte Carlo metode.

• Keywords: information geometry; nuclear structure models
• Keywords (croatian): informacijska geometrija; model nuklearne strukture
• Language: english
• URN:NBN: urn:nbn:hr:217:786386
• Promotion: 2023
• Project: Number: TTP-2018-07-3554; Title: Exotic Nuclear Structure and Dynamics; Title: Exotic Nuclear Structure and Dynamics; Acronym: ExoNSD; Leader: Kosuke Nomura; Jurisdiction: Croatia; Funder: HRZZ; Funding stream: TTP
• Study programme: Title: Doctoral study; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti u području prirodnih znanosti (doktor/doktorica znanosti u području prirodnih znanosti)
• Type of resource: Text
• Extent: 90 str.
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-11-21 13:38:39