Theses and Dissertations from UMD
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New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a give thesis/dissertation in DRUM
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Item Combining Physics-based Modeling, Machine Learning, and Data Assimilation for Forecasting Large, Complex, Spatiotemporally Chaotic Systems(2023) Wikner, Alexander Paul; Ott, Edward; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We consider the challenging problem of forecasting high-dimensional, spatiotemporally chaotic systems. We are primarily interested in the problem of forecasting the dynamics of the earth's atmosphere and oceans, where one seeks forecasts that (a) accurately reproduce the true system trajectory in the short-term, as desired in weather forecasting, and that (b) correctly capture the long-term ergodic properties of the true system, as desired in climate modeling. We aim to leverage two types of information in making our forecasts: incomplete scientific knowledge in the form of an imperfect forecast model, and past observations of the true system state that may be sparse and/or noisy. In this thesis, we ask if machine learning (ML) and data assimilation (DA) can be used to combine observational information with a physical knowledge-based forecast model to produce accurate short-term forecasts and consistent long-term climate dynamics. We first describe and demonstrate a technique called Combined Hybrid-Parallel Prediction (CHyPP) that combines a global knowledge-based model with a parallel ML architecture consisting of many reservoir computers and trained using complete observations of the system's past evolution. Using the Kuramoto-Sivashinsky equation as our test model, we demonstrate that this technique produces more accurate short-term forecasts than either the knowledge-based or the ML component model acting alone and is scalable to large spatial domains. We further demonstrate using the multi-scale Lorenz Model 3 that CHyPP can incorporate the effect of unresolved short-scale dynamics (subgrid-scale closure). We next demonstrate how DA, in the form of the Ensemble Transform Kalman Filter (ETKF), can be used to extend the Hybrid ML approach to the case where our system observations are sparse and noisy. Using a novel iterative scheme, we show that DA can be used to obtain training data for successive generations of hybrid ML models, improving the forecast accuracy and the estimate of the full system state over that obtained using the imperfect knowledge-based model. Finally, we explore the commonly used technique of adding observational noise to the ML model input during training to improve long-term stability and climate replication. We develop a novel training technique, Linearized Multi-Noise Training (LMNT), that approximates the effect of this noise addition. We demonstrate that reservoir computers trained with noise or LMNT regularization are stable and replicate the true system climate, while LMNT allows for greater ease of regularization parameter tuning when using reservoir computers.Item RESPONSE CONTROL IN NONLINEAR SYSTEMS WITH NOISE(2019) Agarwal, Vipin Kumar; Balachandran, Balakumar; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Noise is unavoidable and/or present in a wide variety of engineering systems. Although considered to be undesirable from certain viewpoints, it can play a useful role in influencing the behavior of nonlinear mechanical and structural systems that have multiple solutions in the form of equilibrium points, periodic solutions, and aperiodic (including chaotic) solutions. The aim of this dissertation work is to discover clues related to noise enabled steering or control for engendering desirable changes in system behavior. A combination of experimental, analytical, and numerical studies have been undertaken on the following: i) shifting of jump-up and jump-down frequencies leading to an eventual collapse of hysteresis observed in the response of a nonlinear oscillator, ii) influence of noise on the chaotic response of a nonlinear system, and iii) noise-induced escape route from a chaotic-attractor. Furthermore, a combination of analytical and numerical studies have been undertaken to understand an extended Jeffcott rotor-stator system and the influence of noise on the system dynamics. Additionally, this dissertation includes work on partial control of chaotic systems under the influence of noise, wherein the trajectories are confined inside a particular region (chaotic attractor) despite the presence of white noise. Maintaining chaotic behavior in systems in the presence of an external disturbance may be desirable and important for the dynamics of certain systems. The proposed algorithm has been shown to be effective for systems with different dimensions. The dissertation outcomes provide answers to the following fundamental questions: i) how can noise influence the long-time responses of mechanical and structural systems and ii) how can noise be used to steer a system response to avoid an undesirable dynamical state. These answers can serve as an important foundation for many industrial applications (e.g., applications with rotor-stator systems) as well.Item Finding Optimal Orbits of Chaotic Systems(2005-12-05) Grant, Angela Elyse; Hunt, Brian R; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Chaotic dynamical systems can exhibit a wide variety of motions, including periodic orbits of arbitrarily large period. We consider the question of which motion is optimal, in the sense that it maximizes the average over time of some given scalar ``performance function." Past work indicates that optimal motions tend to be periodic orbits with low period, but does not describe, beyond a brute force approach, how to determine which orbit is optimal in a particular scenario. For one-dimensional expanding maps and higher dimensional hyperbolic systems, we have found constructive methods for calculating the optimal average and corresponding periodic orbit, and by carrying them out on a computer have found them to work quite well in practice.