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Applied Mathematics Theses and Dissertations

Theses and Dissertations for the Applied Mathematics department.

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Items (1-10) out of 10 results

A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding

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
Full Record

Efficient Algorithms for High-Dimensional Hamilton-Jacobi Partial Differential Equations and Optimal Control Problems

Description:
Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections to a wide range of scientific disciplines including optimal control, differential games, imaging sciences, and machine …
Year:
2023
Contributor:
Chen, Paula (creator)
Darbon, Jerome (Advisor)
Shu, Chi-Wang (Reader)
Hewer, Gary (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Field programmable gate arrays
Regression analysis
optimal control
Hamilton-Jacobi equations
Riccati equation
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Generative Adversarial Networks for Physics-Informed Learning

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
Full Record

Interpretable Probabilistic Methods for Genetic Association Mapping and Shape Generation

Description:
As data structures become larger and more complex, methods of data analysis must evolve to harness the most accurate insights. Inspired by the challenges presented …
Year:
2024
Contributor:
Winn-Nunez, Emily Taylor (creator)
Crawford, Lorin (Advisor)
Sandstede, Bjorn (Reader)
Wong, Ian (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Applied mathematics
Shape
Computational biology
nonlinear model fitting
topological data analysis
Quantitative genetics
Bayesian Statistics
Computational modeling
Generative Models
Shapes
Ranking and selection (Statistics)
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Multiscale and Mesoscopic Modeling of Soft Matter and Biophysical Systems Using High Performance Computing and Machine Learning

Description:
This dissertation is composed around the subject of multiscale modeling of soft matter and biophysical systems with applications using large-scale computations. Specifically, it is expanded …
Year:
2017
Contributor:
Tang, Yu-Hang (creator)
Karniadakis, George (Advisor)
Maxey, Martin (Reader)
Baker, Nathan (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Polymers
Biophysics
Scientific Computation
High performance computing
Polymeric drug delivery systems
Soft Matter
Molecular dynamics--Computer simulation
Graphics Processing Units (GPU)
Force Field
Computer simulation
Multiscale modeling
Parallel programming
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Quantifying Patterns in Dynamical Systems and Biological Data

Description:
From data clusters to fish swarms, patterns are widespread in both the natural world and in the era of big data. Across a range of …
Year:
2020
Contributor:
McGuirl, Melissa Rose (creator)
Sandstede, Bjorn (Advisor)
Blumberg, Andrew (Reader)
Harrison, Matthew (Reader)
Ramachandran, Sohini (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Genetics
Patterns
agent-based models
spiral waves
topological data analysis
pattern quantification
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Scientific Machine Learning for Mechanics and Beyond

Description:
This dissertation presents a comprehensive, systematic investigation of methods and applications of scientific machine learning (SciML) in mechanics and their broader implications for interdisciplinary research. …
Year:
2023
Contributor:
Zhang, Enrui (creator)
Humphrey, Jay (Reader)
Srivastava, Vikas (Reader)
Karniadakis, George (Advisor)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Biomechanics
Solid Mechanics
Differential equations--Numerical solutions
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Statistical Learning Tools for Information Fusion in Computational Fluid Dynamics

Description:
For more than a decade, remarkable scientific progress in computational fluid dynamics (CFD) has been achieved via powerful collection of tools for exascale simulations, data-driven …
Year:
2017
Contributor:
Lee, Seungjoon (creator)
Karniadakis, George (Advisor)
Kevrekidis, Ioannis (Advisor)
Maxey, Martin (Reader)
Perdikaris, Paris (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Domain Decomposition methods
Computational fluid dynamics
Gappy data
Exascale simulation
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Stochastic Modeling of Data-driven Complex Systems Using Machine Learning Tools

Description:
This dissertation is composed around the subject of modeling data-driven stochastic complex systems, where there are two challenges: information fusion and uncertainty quantification. In this …
Year:
2019
Contributor:
Zhang, Dongkun (creator)
Karniadakis, George (Advisor)
Wang, Hui (Reader)
Sapsis, Themistoklis (Reader)
Babaee, Hessam (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
Full Record

Theory and Computation for Modern Probabilistic Models

Description:
Modern probabilistic models involve computation and analysis in very high-dimensional spaces. Here we explore several of ways in which analysis of problems high dimensional spaces …
Year:
2017
Contributor:
Loper, Jackson Hoy (creator)
Geman, Stuart (Advisor)
Ramanan, Kavita (Reader)
Harrison, Matthew (Reader)
Brown University. Department of Applied Mathematics (sponsor)
Genre:
theses
Subject:
Machine Learning
Poisson processes
Biometry
Brownian motion processes
Collection:
Applied Mathematics
Theses and Dissertations
Full Record

Items (1-10) out of 10 results