Moderne metode asimilacije podataka - numeričke implementacije i primjene

master's thesis

• Title (english): Modern methods of data assimilation - numerical implementations and applications
• Author: Juraj Bilušković
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Committee member: Matko Ljulj (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2023-07-17, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad predstavio je teoriju asimilacije podataka te ju primijenio na konkretnom problemu. Asimilacija podataka relativno je novo i interdisciplinarno područje koje se i dalje razvija. To je metoda koja kombinira opservacije stanja sustava s rezultatima modela kako bi se poboljšala procjena stanja sustava pa samim time i rezultati modela. Koristeći asimilaciju podataka napravljene su predikcije širenja zaraze COVID-19 u Hrvatskoj. Prvotno je iznesena matematička teorija potrebna za daljnju izgradnju matematičkih modela i algoritama asimilacije podataka. Obrađeni su osnovni pojmovi iz teorije vjerojatnosti s naglaskom na Bayesovskoj statistici, teorije dinamičkih sustava s naglaskom na dinamičke sustave s kontrolom i numeričkog rješavanja inicijalnog problema sustava običnih diferencijalnih jednadžbi.

Abstract (english)

This work presented the theory of data assimilation and applied it to a concrete problem. Data assimilation is a relatively new and interdisciplinary field which is still developing. It is a method that combines the observations of the system state with model results to improve the estimation of the system state and thus the model results. Predictions of the spread of the COVID-19 infection in Croatia are made using data assimilation. Firstly, mathematical theory needed for further development of mathematical models and data assimilation algorithms is carried out. Basic terms from probability theory focusing on Bayesian statistics, dynamical systems theory focusing on controlled dynamical systems and numerical solving initial-value problems of ordinary differential equations are introduced.

• Keywords: zaraza COVID-19; Hrvatska; algoritmi asimilacije podataka; teorija vjerojatnosti; Bayesovsa statistika
• Keywords (english): COVID-19 infection; Croatia; data assimilation algorithms; probability theory; Bayesian statistics
• Language: croatian
• URN:NBN: urn:nbn:hr:217:726303
• Study programme: Title: Financial and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: sveučilišni magistar matematike (sveučilišni magistar matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-08 12:14:24