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.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etd-5857 |
| Date | 01 December 2023 |
| Creators | Borquaye, Noah |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
| Rights | Copyright by the authors. |
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