Reduced order modelling of diffussion-reaction partial differential equations

This doctoral thesis consists of five main parts. The first chapter is the introduction and states the importance of the thesis with a literature review. In the second chapter, Diffusion-Reaction Partial Differential Equation systems are introduced, related examples are given, and some important properties and application of Principal Component Analysis are explained. In the third section, Kernel Principal Component Analysis is introduced. In the fourth part, examples for each class of Diffusion-Reaction Partial Differential Equation systems are analyzed. In the Conclusion and Recommendations section, the findings of the study are evaluated and ideas for future studies are presented.