Learning Reduced-Order Mappings between Functions

An Investigation of Suitable Inputs and Outputs

Bachelor Thesis (2024)
Author(s)

B. Bakker (TU Delft - Electrical Engineering, Mathematics and Computer Science)

Contributor(s)

M. Naderibeni – Mentor (TU Delft - Pattern Recognition and Bioinformatics)

David Tax – Mentor (TU Delft - Pattern Recognition and Bioinformatics)

N. Tömen – Graduation committee member (TU Delft - Pattern Recognition and Bioinformatics)

Faculty
Electrical Engineering, Mathematics and Computer Science
Copyright
© 2024 Bo Bakker
More Info
expand_more
Publication Year
2024
Language
English
Copyright
© 2024 Bo Bakker
Graduation Date
02-02-2024
Awarding Institution
Delft University of Technology
Project
CSE3000 Research Project
Programme
Computer Science and Engineering
Faculty
Electrical Engineering, Mathematics and Computer Science
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Abstract

Data-driven approaches are a promising new addition to the list of available strategies for solving Partial Differential Equations (PDEs). One such approach, the Principal Component Analysis-based Neural Network PDE solver, can be used to learn a mapping between two function spaces, corresponding to a PDE. However, the practical limitations of this approach are unclear. This paper seeks to investigate for which types of inputs and outputs this type of solver gives useful results. Using a dataset with inputs sampled from Gaussian Random Fields with different parameters, and outputs for Poisson's equation and the Heat equation, obtained by using a Finite Element solver, neural networks are trained, and their performance is evaluated. The method performs adequately for the chosen inputs, and patterns are found in the resulting error, which differ for each set of input parameters. Thus, for these equations, it seems that this method performs differently for different input distributions, but further research is necessary to investigate if these patterns will hold for other equations.

Files

CSE3000_Bakker.pdf
(pdf | 2.8 Mb)
License info not available