The overarching goal of this project is to develop intelligent, self-adapting numerical algorithms for the time discretization of complex real-world problems with Q-Learning methodologies. The specific application is ordinary differential equations which can resolve problems in mathematics, social and natural sciences, but which usually require approximations to solve because direct analytical solutions are rare. Using the traditional Brusellator and Lorenz differential equations as test beds, this research develops models to determine reward functions and dynamically tunes controller parameters that minimize both the error and number of steps required for approximate mathematical solutions. Our best reward function is based on an error that does not overly punish rejected states. The Alpha-Beta Adjustment and Safety Factor Adjustment Model is the most efficient and accurate method for solving these mathematical problems. Allowing the model to change the alpha/beta value and safety factor by small amounts provides better results than if the model chose values from discrete lists. This method shows potential for training dynamic controllers with Reinforcement Learning. / Master of Science / This research applies Q-Learning, a subset of Reinforcement Learning and Machine Learning, to solve complex mathematical problems that are unable to be solved analytically and therefore require approximate solutions. Specifically, this research applies mathematical modeling of ordinary differential equations which are used in many fields, from theoretical sciences such and physics and chemistry, to applied technical fields such as medicine and engineering, to social and consumer-oriented fields such as finance and consumer purchasing habits, and to the realms of national and international security and communications. Q-Learning develops mathematical models that make decisions, and depending on the outcome, learns if the decision is good or bad, and uses this information to make the next decision. The research develops approaches to determine reward functions and controller parameters that minimize the error and number of steps associated with approximate mathematical solutions to ordinary differential equations. Error is how far the model's answer is from the true answer, and the number of steps is related to how long it takes and how much computational time and cost is associated with the solution. The Alpha-Beta Adjustment and Safety Factor Adjustment Model is the most efficient and accurate method for solving these mathematical problems and has potential for solving complex mathematical and societal problems.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/113865 |
| Date | 27 August 2021 |
| Creators | Gallagher, Conor Dietrich |
| Contributors | Computer Science, Sandu, Adrian, Gulzar, Muhammad Ali, Karpatne, Anuj |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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