Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
12-2023
Committee Chair or Co-Chairs
Jeff R. Knisley
Committee Members
Michele L. Joyner, Mostafa Zahed, Stephen E. Moore
Abstract
Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to system identification and forecasting of solutions of nonlinear differential equations by replacing matrix multiplication with convolution transformation. In particular, we develop convolution-based approach to dynamic mode decomposition and discuss its application to problems not solvable otherwise.
Document Type
Thesis - unrestricted
Recommended Citation
Borquaye, Noah, "Convolution and Autoencoders Applied to Nonlinear Differential Equations" (2023). Electronic Theses and Dissertations. Paper 4315. https://dc.etsu.edu/etd/4315
Copyright
Copyright by the authors.
Included in
Applied Mathematics Commons, Computational Engineering Commons, Computer Engineering Commons, Data Science Commons, Dynamical Systems Commons, Education Commons, Other Mathematics Commons, Other Physical Sciences and Mathematics Commons, Systems Science Commons