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Author:

Thornton, Stephen

Title:

Helical Symmetry Solutions to the Equations of Magnetohydrodynamics

Area of Honors:

Mathematics

Keywords:

Magnetohydrodynamics
MHD
Fluids
PDE
Partial Differential Equations

File:

Download ThorntonFinalMathThesis.pdf

Thesis Supervisors:

Anna L Mazzucato, Thesis Supervisor
Ludmil Tomov Zikatanov, Thesis Honors Advisor

Author:

Liang, Fei

Title:

A new training method for neural network in solving PDEs

Area of Honors:

Mathematics

Keywords:

Neural Network
PDE
Deep-Ritz
training method
efficiency

File:

Download A_New_Training_Method_for_Deep_Neural_Network_in_Solving_PDEs.pdf

Thesis Supervisors:

Xiantao Li, Thesis Supervisor
Xiantao Li, Thesis Honors Advisor
Wenrui Hao, Faculty Reader

Author:

Hanafi, Ashhad

Title:

Modeling Microbubble Motion in Poiseuille Flow Using Neural Networks: A Comparative Study of Physics-Informed, Data-Driven, and Hybrid Approaches

Area of Honors:

Computer Science

Keywords:

neural networks
neural network
flow
microbubble
microbubbles
bubbles
bubble
pinn
physics-informed
data
data-driven
BUFF
flow field
loss
MSE
trajectory
poiseuille
network
neural
PDE
ODE
differential
equations
equation
physics
machine
learning
machine learning

File:

Download thesis-updated.pdf

Thesis Supervisors:

Mohamed Khaled Almekkawy, Thesis Supervisor
Rebecca Jane Passonneau, Thesis Honors Advisor