UMD Theses and Dissertations
Permanent URI for this collectionhttp://hdl.handle.net/1903/3
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 given thesis/dissertation in DRUM.
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Item Dynamical Memory in Deep Neural Networks -(2024) Evanusa, Matthew S; Aloimonos, Yiannis; Computer Science; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this work, I will begin to lay out a roadmap or framework for which I believe will serve the scientific communities of artificial intelligence and cognitive neuroscience of interest, in future development and design of a thinking intelligent machine, based on the accumulated knowledge I have gathered across many sources: from my advisors, peers and colleagues, collaborators, talks, symposia and conferences, and long paper dives, for the almost decade that I have spent at my new home in College Park, Maryland. It is my hope and intent that this thesis serves in its stated goal to advance the science of memory integration in neural networks, but in addition, to further the distant dream of discovering the mystery of what it means to be alive. It is important to note that while this thesis is focused on the critical integration of memory mechanisms into artificial neural networks, the authors’ larger goal is the creation of an overarching cognitive architecture that takes advantages of the right amount of advances from deep learning, with the right amount of insights from cognitive and neuroscience - a ”Goldilocks” of sorts for AI. It is my hope that through understanding mechanisms of memory and how they interact with our stimluli, we move one step closer to understanding our place in the cosmos.Item Learning in Large Multi-Agent Systems(2024) Kara, Semih; Martins, Nuno C; Electrical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we study a framework of large-scale multi-agent strategic interactions. The agents are nondescript and use a learning rule to repeatedly revise their strategies based on their payoffs. Within this setting, our results are structured around three main themes: (i) Guaranteed learning of Nash equilibria, (ii) The inverse problem, i.e. estimating the payoff mechanism from the agents' strategy choices, and (iii) Applications to the placement of electric vehicle charging stations. In the traditional setup, the agents' inter-revision times follow identical and independent exponential distributions. We expand on this by allowing these intervals to depend on the agents' strategies or have Erlang distributions. These extensions enhance the framework's modeling capabilities, enabling it to address problems such as task allocation with varying service times or multiple stages. We also explore a third generalization, concerning the accessibility among strategies. Majority of the existing literature assume that the agents can transition between any two strategies, whereas we allow only certain alternatives to be accessible from certain others. This adjustment further improves the framework's modeling capabilities, such as by incorporating constraints on strategy switching related to spatial and informational factors. For all of these extensions, we use Lyapunov's method and passivity-based techniques to find conditions on the revision rates, learning rule, and payoff mechanism that ensure the agents learn to play a Nash equilibrium of the payoff mechanism. For our second class of problems, we adopt a multi-agent inverse reinforcement learning perspective. Here, we assume that the learning rule is known but, unlike in existing work, the payoff mechanism is unknown. We propose a method to estimate the unknown payoff mechanism from sample path observations of the populations' strategy profile. Our approach is two-fold: We estimate the agents' strategy transitioning probabilities, which we then use - along with the known learning rule - to obtain a payoff mechanism estimate. Our findings regarding the estimation of transitioning probabilities are general, while for the second step, we focus on linear payoff mechanisms and three well-known learning rules (Smith, replicator, and Brown-von Neumann-Nash). Additionally, under certain assumptions, we show that we can use the payoff mechanism estimate to predict the Nash equilibria of the unknown mechanism and forecast the strategy profile induced by other rules. Lastly, we contribute to a traffic simulation tool by integrating electric vehicles, their charging behaviors, and charging stations. This simulation tool is based on spatial-queueing principles and, although less detailed than some microscopic simulators, it runs much faster and accurately represents traffic rules. Using this tool, we identify optimal charging station locations (on real roadway networks) that minimize the overall traffic.Item A Time Parallel Approach to Numerical Simulation of Asymptotically Stable Dynamical Systems with Application to CFD Models of Helicopter Rotors(2023) Silbaugh, Benjamin Scott; Baeder, James D; Aerospace Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Modern High Performance Computing (HPC) machines are distributed memoryclusters, consisting of multi-core compute nodes. Engineering simulation and analysis tools must employ efficient parallel algorithms in order to fully utilize the compute capability of modern HPC machines. The trend in Computational Fluid Dynamcis (CFD) has been to construct parallel solution algorithms based on some form of spatial domain decomposition. This approach has been shown to be a success for many practical applications. However, as one attempts to utlize more compute cores, limitations in strong scalability are inevitably reached due to a diminishing compute workload per compute core and either fixed or increasing communication cost. Furthermore, spatial domain decomposition approaches cannot be easily applied to mid-fidelity structural dynamics or rigid body dynamics models. A significant majority of industrial fluid and structural dynamic models utilize some form of time marching. Thus, if the domain decomposition strategy may be extended to include the temporal dimension, additional opportunity for increased parallelism may be realized. A new form of periodic multiple shooting is proposed that ismatrix-free and may be applied to high-fidelity multiphysics models or other high dimensional systems. The proposed methodology is formulated entirely in the time domain. Therefore, existing time-domain simulation tools may utilize the proposed approach to achieve a high degree of distributed memory parallelism without requiring any reformulation. Furthermore, the proposed methodology may be combined with conventional space domain decomposition techniques and other forms of data parallelism to achieve maximal performance on modern HPC architectures. The proposed algorithm retains the iterative shoot-correct approach of conventational periodic shooting methods. However, the correction stage is formulated using a hierarchical evaluation strategy combined with an Arnoldi subspace approximation to eliminate the need for explicit formulation of Jacobian matricies. The local convergence of the proposed method is formally proven for the case of an asyptotically stable dynamical system. The proposed method is numerically tested for a 2D limit cycle problem, a rigid blade helicoper rotor model with quasi-steady aerodynamics and autopilot trim, and an OVERSET CFD model of a helicopter rotor with prescribed elastic blade motions. The method is observed to be convergent in all test cases and found to exhibit good scalability. The proposed periodic multiple shooting method is a practical means of reducingtime-to-solution for numerical simulations of asymptotically stable periodic systems on distributed memory parallel computers. Furthermore, the proposed method may be used to enhance the parallel scalability of OVERSET CFD models of helicopter rotors in steady periodic flight.Item DEVELOPING MACHINE LEARNING TECHNIQUES FOR NETWORK CONNECTIVITY INFERENCE FROM TIME-SERIES DATA(2022) Banerjee, Amitava; Ott, Edward; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Inference of the connectivity structure of a network from the observed dynamics of the states of its nodes is a key issue in science, with wide-ranging applications such as determination of the synapses in nervous systems, mapping of interactions between genes and proteins in biochemical networks, distinguishing ecological relationships between different species in their habitats etc. In this thesis, we show that certain machine learning models, trained for the forecasting of experimental and synthetic time-series data from complex systems, can automatically learn the causal networks underlying such complex systems. Based on this observation, we develop new machine learning techniques for inference of causal interaction network connectivity structures underlying large, networked, noisy, complex dynamical systems, solely from the time-series of their nodal states. In particular, our approach is to first train a type of machine learning architecture, known as the ‘reservoir computer’, to mimic the measured dynamics of an unknown network. We then use the trained reservoir computer system as an in silico computational model of the unknown network to estimate how small changes in nodal states propagate in time across that network. Since small perturbations of network nodal states are expected to spread along the links of the network, the estimated propagation of nodal state perturbations reveal the connections of the unknown network. Our technique is noninvasive, but is motivated by the widely used invasive network inference method, whereby the temporal propagation of active perturbations applied to the network nodes are observed and employed to infer the network links (e.g., tracing the effects of knocking down multiple genes, one at a time, can be used infer gene regulatory networks). We discuss how we can further apply this methodology to infer causal network structures underlying different time-series datasets and compare the inferred network with the ground truth whenever available. We shall demonstrate three practical applications of this network inference procedure in (1) inference of network link strengths from time-series data of coupled, noisy Lorenz oscillators, (2) inference of time-delayed feedback couplings in opto-electronic oscillator circuit networks designed the laboratory, and, (3) inference of the synaptic network from publicly-available calcium fluorescence time-series data of C. elegans neurons. In all examples, we also explain how experimental factors like noise level, sampling time, and measurement duration systematically affect causal inference from experimental data. The results show that synchronization and strong correlation among the dynamics of different nodal states are, in general, detrimental for causal network inference. Features that break synchrony among the nodal states, e.g., coupling strength, network topology, dynamical noise, and heterogeneity of the parameters of individual nodes, help the network inference. In fact, we show in this thesis that, for parameter regimes where the network nodal states are not synchronized, we can often achieve perfect causal network inference from simulated and experimental time-series data, using machine learning techniques, in a wide variety of physical systems. In cases where effects like observational noise, large sampling time, or small sampling duration hinder such perfect network inference, we show that it is possible to utilize specially-designed surrogate time-series data for assigning statistical confidence to individual inferred network links. Given the general applicability of our machine learning methodology in time-series prediction and network inference, we anticipate that such techniques can be used for better model-building, forecasting, and control of complex systems in nature and in the lab.Item Quantifying Dynamic Pitch Adjustment Decision Structures in String Quartet Performance(2021) Tavani, Nicholas John; Salness, David; Music; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)What does it mean to have a unique group sound? Is such a thing quantifiable? If so, are there noticeable differences between groups, and any correlations to the time each group spends together? It is important to note a caveat right off the bat: music is generally understood to be created by and listened to by humans, and thus any attempts at quantifiable answers to the above questions will be, at best, orthogonal to its main purpose. It is also clear from anecdotes and interviews with professional musicians that qualitatively distinguishable characteristics of group sound and interpretation absolutely do exist and are noticeable to the listener. Paul Katz, cellist of the Cleveland Quartet, describes the multiple layers of such a group identity: “When one spends that many hours per day and years together, there is a meshing of taste, an unspoken unification of musical values, an intuitive understanding of each other's timings and shapings, and even a merging of how one produces sounds, makes a bow change, or varies vibrato, that is deeper than words or conscious decision making.” This dissertation concerns itself with the general question of whether or not it is possible to detect and define, in a quantifiable sense, the patterns and elements of a unique group sound identity, specifically in the intonation domain. Original research was carried out, consisting of recording four string quartets with high-quality equipment under controlled conditions, to begin to answer this question.Item UNCOVERING PATTERNS IN COMPLEX DATA WITH RESERVOIR COMPUTING AND NETWORK ANALYTICS: A DYNAMICAL SYSTEMS APPROACH(2020) Krishnagopal, Sanjukta; Girvan, Michelle; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we explore methods of uncovering underlying patterns in complex data, and making predictions, through machine learning and network science. With the availability of more data, machine learning for data analysis has advanced rapidly. However, there is a general lack of approaches that might allow us to 'open the black box'. In the machine learning part of this thesis, we primarily use an architecture called Reservoir Computing for time-series prediction and image classification, while exploring how information is encoded in the reservoir dynamics. First, we investigate the ways in which a Reservoir Computer (RC) learns concepts such as 'similar' and 'different', and relationships such as 'blurring', 'rotation' etc. between image pairs, and generalizes these concepts to different classes unseen during training. We observe that the high dimensional reservoir dynamics display different patterns for different relationships. This clustering allows RCs to perform significantly better in generalization with limited training compared with state-of-the-art pair-based convolutional/deep Siamese Neural Networks. Second, we demonstrate the utility of an RC in the separation of superimposed chaotic signals. We assume no knowledge of the dynamical equations that produce the signals, and require only that the training data consist of finite time samples of the component signals. We find that our method significantly outperforms the optimal linear solution to the separation problem, the Wiener filter. To understand how representations of signals are encoded in an RC during learning, we study its dynamical properties when trained to predict chaotic Lorenz signals. We do so by using a novel, mathematical fixed-point-finding technique called directional fibers. We find that, after training, the high dimensional RC dynamics includes fixed points that map to the known Lorenz fixed points, but the RC also has spurious fixed points, which are relevant to how its predictions break down. While machine learning is a useful data processing tool, its success often relies on a useful representation of the system's information. In contrast, systems with a large numbers of interacting components may be better analyzed by modeling them as networks. While numerous advances in network science have helped us analyze such systems, tools that identify properties on networks modeling multi-variate time-evolving data (such as disease data) are limited. We close this gap by introducing a novel data-driven, network-based Trajectory Profile Clustering (TPC) algorithm for 1) identification of disease subtypes and 2) early prediction of subtype/disease progression patterns. TPC identifies subtypes by clustering patients with similar disease trajectory profiles derived from bipartite patient-variable networks. Applying TPC to a Parkinson’s dataset, we identify 3 distinct subtypes. Additionally, we show that TPC predicts disease subtype 4 years in advance with 74% accuracy.Item Absolutely Continuous Spectrum for Parabolic Flows/Maps(2016) Simonelli, Lucia Dora; Forni, Giovanni; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely continuous spectral measures. We use these general conditions to derive results for spectral properties of time-changes of unipotent flows on homogeneous spaces of semisimple groups regarding absolutely continuous spectrum as well as maximal spectral type; the time-changes of the horocycle flow are special cases of this general category of flows. In addition we use the general conditions to derive spectral results for twisted horocycle flows and to rederive spectral results for skew products over translations and Furstenberg transformations.Item Progress Toward Classifying Teichmueller Disks with Completely Degenerate Kontsevich-Zorich Spectrum(2012) Aulicino, David; Forni, Giovanni; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We present results toward resolving a question posed by Eskin-Kontsevich-Zorich and Forni-Matheus-Zorich. They asked for a classification of all $\text{SL}_2(\mathbb{R})$-invariant ergodic probability measures with completely degenerate Kontsevich - Zorich spectrum. Let $\mathcal{D}_g(1)$ be the subset of the moduli space of Abelian differentials $mathcal{M}_g$ whose elements have period matrix derivative of rank one. There is an $\text{SL}_2(\mathbb{R})$-invariant ergodic probability measure $nu$ with completely degenerate Kontsevich-Zorich spectrum, i.e. $lambda_1 = 1 > lambda_2 = cdots = lambda_g = 0$, if and only if $nu$ has support contained in $\mathcal{D}_g(1)$. We approach this problem by studying Teichm"uller disks contained in $\mathcal{D}_g(1)$. We show that if $(X,omega)$ generates a Teichm"uller disk in $\mathcal{D}_g(1)$, then $(X,omega)$ is completely periodic. Furthermore, we show that there are no Teichm"uller disks in $\mathcal{D}_g(1)$, for $g = 2$, and the known example of a Teichm"uller disk in $mathcal{D}_3(1)$ is the only one. Finally, we present an idea that might be able to fully resolve the problem.Item The Cohomological Equation for Horocycle Maps and Quantitative Equidistribution(2011) Tanis, James Holloway; Forni, Giovanni; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)There are infinitely many distributional obstructions to the existence of smooth solutions for the cohomological equation u o φ1 - u = f in each irreducible component of L2(Γ\PSL(2,R)), where φ1 is the time-one map of the horocycle flow. We study the regularity of these obstructions, determine which ones also obstruct the existence of L2 solutions and prove a Sobolev estimate of the solution in terms of f. As an application, we estimate the rate of equidistribution of horocycle maps on compact, finite volume manifolds Γ\PSL(2,R)) using an auxiliary result from Flaminio-Forni (2003) and one from Venkatesh (2010) concerning the horocycle flow and the twisted horocycle flow, respectively.Item Cometary Escape in the Restricted Circular Planar Three Body Problem(2011) Galante, Joseph Robert; Kaloshin, Vadim Yu; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The classical principle of least action says that orbits of mechanical systems extremize action; an important subclass are those orbits that minimize action. This principle is utilized along with Aubry-Mather theory to construct regions of instability for a certain three body problem, given by a Hamiltonian system of two degrees of freedom. In principle, these methods can be applied to construct instability regions for a variety of Hamiltonian systems with $2$ degrees of freedom. The Hamiltonian model considered in this thesis describes the dynamics of a Sun-Jupiter-Comet system and under some simplifying assumptions, the existence of instabilities for the orbit of the comet is shown. In particular it is shown that a comet which starts close to an orbit in the shape of an ellipse of eccentricity $e=0.66$ can increase in eccentricity to beyond $e=1$. Furthermore, there exist ejection orbits for the comet. Such orbits are initially well within the range of our solar system. This might give an indication of why most objects rotating around the Sun in our solar system have relatively low eccentricity. Several new theoretical tools are introduced in this thesis as well. The most notable is a checkable sufficient condition to verify that an exact area preserving map is an exact area preserving twist map in a certain coordinate system. This coordinate system is constructed by ``spreading the cumulative twist'' which arises from the long term dynamics of system. Many of the results of the thesis are `computer assisted' and utilize recent advances in rigorous numerical integration. It is through the application of these advances in computing that it has become possible to state deep results for realistic solar systems. This has been the dream of many since humans first observed the stars so long ago.