Inverse problems, foundational in applied sciences, involve deducing system inputs from specific output observations. These problems find applications in diverse domains such as aerospace engineering, weather prediction, and oceanography. However, their solution often requires complex numerical simulations and substantial computational resources. Modern machine learning based approaches have emerged as an alternative and flexible methodology for solving these types of problems, however their generalization power often comes at the cost of working with large descriptive datasets, a requirement that many applications cannot afford. This thesis proposes and explores the novel Deep Multi-resolution Operator Network (DMON), inspired by the recently developed DeepONet architecture. The DMON model is designed to solve inverse problems related to chaotic non-linear systems with low-resolution data through intelligently utilizing high-resolution data from a similar system. Performance of the DMON model and the proposed selection mechanisms are evaluated on two chaotic systems, a double pendulum and turbulent flow around a cylinder, with improvements observed under idealized scenarios whereby high and low-resolution inputs are manually paired, along with minor improvements when this pairing is conducted through the proposed the latent space comparison selection mechanism. / Master of Science / In everyday life, we often encounter the challenge of determining the cause behind something we observe. For instance, meteorologists infer weather patterns based on limited atmospheric data, while doctors use X-rays and CT scans to reconstruct images representing the insides of our bodies. Solving these so called ``inverse problems'' can be difficult, particularly when the process is chaotic such as the weather, whereby small changes result in much larger ones over time. In this thesis, we propose a novel method using artificial intelligence and high-resolution simulation data to aid in solving these types of problems. Our proposed method is designed to work well even when we only have access to a small amount of information, or the information available isn't very detailed. Because of this there are potential applications of the proposed method across a wide range of fields, particularly those where acquiring detailed information is difficult, expensive, or impossible.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/117339 |
| Date | 11 January 2024 |
| Creators | Donald, Sam Alexander Knowles |
| Contributors | Computer Science & Applications, Sandu, Adrian, Lourentzou, Ismini, Karpatne, Anuj |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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