Bachelor's Thesis in Mathematical Engineering

Title

Decomposizione ai valori singolari di una matrice e applicazioni alla Dynamic Mode Decomposition

Author

Federico Riva

Supervisor

Professor Marco Verani

Overview

This repository contains the materials for my final thesis in Mathematical Engineering, completed under the supervision of Professor Marco Verani. The thesis focuses on Singular Value Decomposition (SVD) and Dynamic Mode Decomposition (DMD), with an application to the SEIRD model (Susceptible-Exposed-Infected-Recovered-Deceased) used for modeling epidemics. Particular attention is given to reducing computational cost by appropriately leveraging matrix properties.

Topics Covered

• Singular Value Decomposition (SVD): A matrix factorization technique that is fundamental in many applications, including data compression, noise reduction, and system analysis.
• Dynamic Mode Decomposition (DMD): A data-driven technique used to extract dynamic patterns from time-series data. DMD provides insight into the underlying dynamics of complex systems.
• SEIRD Model Application: The SVD and DMD methods were applied to the SEIRD model, which is used to describe the dynamics of infectious disease spread. This application demonstrates the power of these techniques in simplifying and analyzing complex systems.

Achievements

I was awarded the maximum score of 7/7 for this thesis.

Contents

The repository includes:

• Thesis Document: The full write-up of the thesis, explaining the methodology, results, and conclusions.
• MATLAB Code: Scripts for performing SVD, DMD, and applying these methods to the SEIRD model.
• Figures and Data: All relevant figures and data used in the thesis analysis.