Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Description:: Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for …
Year:: 2019
Contributor:: Burkhart, Michael C. (creator); Harrison, Matthew (Advisor); Gidas, Basilis (Reader); Darbon, Jerome (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Machine Learning; Brain-computer interfaces; Gaussian processes; Bayesian filtering; Supervised learning (Machine learning); Neural decoding; Hidden Markov models; State-space models; Neural networks (Computer science); Computational neuroscience; Discriminative probabilistic modeling; Nonparametric statistics
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: This thesis consists of two topics on discontinuous Galerkin (DG) finite element methods for time-dependent problems. In the first part of the thesis, we analyze …
Year:: 2018
Contributor:: Sun, Zheng (creator); Shu, Chi-Wang (Advisor); Guzman, Johnny (Reader); Darbon, Jerome (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Numerical Anlaysis; Scientific Computation; Discontinuous Galerkin Methods; Time Discretization Methods; Gradient Flow Problems
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Motivated by the ubiquitous demand of leveraging both data and partial knowledge of physical laws for stochastic modeling and uncertainty quantification, in the dissertation, a …
Year:: 2021
Contributor:: Yang, Liu (creator); Karniadakis, George (Advisor); Perdikaris, Paris (Reader); Darbon, Jerome (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Machine Learning; Data-Driven Scientific Computing; Uncertainty Quantification
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: This dissertation presents two topics on numerical solutions solving hyperbolic equations from both theoretical and practical points of view. In the first part, we introduce …
Year:: 2018
Contributor:: Shi, Cengke (creator); Shu, Chi-Wang (Advisor); Guzman, Johnny (Reader); Darbon, Jerome (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Discontinuous Galerkin Methods; Numerical analysis; hyperbolic conservation law
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: The positivity-preserving property is a highly desirable property when designing high order numerical methods for hyperbolic conservation laws, since negative values sometimes cause ill-posedness of …
Year:: 2017
Contributor:: Qin, Tong (creator); Shu, Chi-Wang (Advisor); Guzman, Johnny (Reader); Darbon, Jerome (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Numerical Anlaysis; Scientific Computation; Positivity Preserving; Implicit Time Stepping; Relativistic Hydrodynamics; Discontinuous Galerkin Methods
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: The Riemannian Langevin Equation is a natural extension of Langevin equation on Riemannian manifolds. As a stochastic relaxation of gradient flow, Riemannian Langevin equation serves …
Year:: 2024
Contributor:: Yu, Tianmin (creator); Menon, Govind (Advisor); Darbon, Jerome (Reader); Shenfeld, Yair (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Applied mathematics
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Rare events are ones which occur infrequently, sometimes with extremely small probability, but they may nevertheless affect pertinent properties of a system. Such rare events …
Year:: 2019
Contributor:: Snarski, Michael (creator); Dupuis, Paul (Advisor); Darbon, Jerome (Reader); Matzavinos, Anastasios (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Limit theorems (Probability theory); Large deviations; Probabilities
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a …
Year:: 2023
Contributor:: Veraszto, Zsolt (creator); Menon, Govind (Advisor); Cohen, Nadav (Reader); Darbon, Jerome (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: generalizability; gradient flows; implicit regularization; rieamannian geometry; matrix completion; deep linear network
Collection:: Applied Mathematics; Theses and Dissertations

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Description:: Uncertainty quantification (UQ) is a critical component in scientific machine learning (SciML), addressing the challenges of modeling, predicting, and interpreting complex systems under incomplete or …
Year:: 2024
Contributor:: Zou, Zongren (creator); Karniadakis, George (Advisor); Darbon, Jerome (Reader); Owhadi, Houman (Reader); Tartakovsky, Daniel (Reader); Brown University. Department of Applied Mathematics (sponsor)
Genre:: theses
Subject:: Applied mathematics
Collection:: Applied Mathematics; Theses and Dissertations

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