dissertation.tex

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\documentclass[11pt]{unc_dissertation}

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\usepackage{import}
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% List of acronyms
\usepackage{longtable}
\usepackage[acronym]{glossaries}

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\usepackage{amsmath}
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\usepackage{titlesec}
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\usepackage{indentfirst}   %Indents first paragraphs in every section.

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\title{Dissertation Title}
\author{Dissertation Author}
\committee{Advisor}{Committee Member}{Committee Member}{Committee Member}{Committee Member}
\date{January 1, 1970}

\input{abstract.tex}

\dedication{To Wawa}

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% GLOSSARIES AND ABBREVIATIONS
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% To update the printed glossary, you need to run:
% - pdflatex dissertation
% - makeglossaries dissertation
% - pdflatex dissertation
% On Windows, you might need to install Perl first.
\newacronym{unc}{UNC}{The University of North Carolina at Chapel Hill}
\makeglossaries

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\linespread{1.0}
\begin{document}

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\ifpdf
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\pagestyle{plain}

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%% INITIAL THINGS
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\frontmatter

\maketitle

\chapter*{Acknowledgements}
\input{acknowledgements.tex}

% The graduate school requires that entries are double spaced.
% They also require that multiple lines in a single entry are single spaced.
% This achieves that by setting \baselineskip (the space between lines)
% and \parskip (the additional space between paragraphs) directly, then restoring them
%
% @todo: Find a more elegant way of achieving this

% Establish original spacings
\newlength{\oldbaselineskip}
\setlength{\oldbaselineskip}{\the\baselineskip}
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\setlength{\baselineskip}{0.5\oldbaselineskip}
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\tableofcontents

\listoffigures

\listoftables

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\setlength{\baselineskip}{1.0\oldbaselineskip}
\setlength{\parskip}{1.0\oldparskip}

\listofabbreviations

\mainmatter

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%MAIN CHAPTERS%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\pagestyle{plain} % Restore page numbers
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% Chapter 0
% Everything, disorganized
\chapter{Chapter 0}
\input{UseCasePINNs.tex}
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% Chapter 1
% Overview of Neural Networks and Supervised (Learning) NN Approximation
\chapter{Chapter 1}
\input{chapter1.tex}
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% Chapter 2
% Brief Introduction to equation-informed (unsupervised) NN approximations to PDEs PINNs, overview of results (forward, backward, identification, SDEs), FFR Application? ROM and surrogate models, 
\chapter{Chapter 2}
\input{chapter2.tex}
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% Chapter 3
% Brief Introduction to equation-informed (unsupervised) NN approximations to PDEs PINNs, overview of results (forward, backward, identification, SDEs), FFR Application?
\chapter{Chapter 3}
\input{chapter2.tex}
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% Chapter 
% 1D Deep LS, Deep FOSLS, Deep Energy Method comparison
\chapter{Chapter 2}
\input{chapter2.tex}
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% Chapter 
% 2D (Unconstrained?) PDEs
% Deep FOSLS vs PINNs comparison.  
% Poisson-like Equations
% Poisson
% Diffusion
% Helmholtz
%
\chapter{Chapter 2}
%laplace
\input{poisson2d.tex}
\input{surfacepoisson2d.tex}
%\input{diffusion2d.tex}
%\input{diffusionreaction2d.tex}
%singularlyperturbed
\input{advectiondiffusionreaction2d.tex}
\input{helmholtz2d.tex}
\input{chapter2.tex}

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% Chapter 
% Introduction: FEM and LSFEM methods
% Linear and Hyperelastic Elasticity
% PINNs vs Deep FOSLS (Deep Energy Method?)comparison
% thesisLeast-squares mixed finite elements for geometricallySteegerDiss.pdf
\chapter{Finite Element Methods and Least-Squares FEM in Solid and Fluid Mechanics}
%\input{Galerkin and mixed Galerkin finite elements.tex}
\input{GalerkinandMixedGalerkinFiniteElements.tex}
%\input{Least-squares mixed finite elements.tex}
\input{LeastSquaresMixedFiniteElements.tex}
%\input{Outline}
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% Chapter 
% 2D Static Solid Mechanics 
% Linear and Hyperelastic Elasticity
% PINNs vs Deep FOSLS (Deep Energy Method?)comparison
% thesisLeast-squares mixed finite elements for geometricallySteegerDiss.pdf
\chapter{Continuum mechanical background}
\input{KinematicsAndDeformationMeasures.tex}
\input{StressQuantities.tex}
\input{Hyperelasticmaterials.tex}
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% Chapter 
% Background: LSFFEM for Steady Newtonian Fluid Mechanics
\chapter{First-Order Systems Least-Squares Formulations of Navier-Stokes Equations for Steady Newtonian Fluid Mechanics}
\input{LinearElasticityPureTractionFormulation.tex}
\input{LinearElasticityPureDisplacementFormulation.tex}
\input{LinearElasticityTractionDisplacementFormulation.tex}
\input{hyperelasticfosls.tex}
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% Chapter 
% Background: LSFFEM for Steady Newtonian Fluid Mechanics
\chapter{First-Order Systems Least-Squares Formulations of Navier-Stokes Equations for Steady Newtonian Fluid Mechanics}
\input{VPFormulation.tex}
\input{VVFormulation.tex}
\input{VVPFormulation.tex}
\input{VPSFormulation.tex}
\input{VVGFormulation.tex}
\input{VVTFormulation.tex}
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% Chapter 
% PINN Approximations to Navier-Stokes: 
% 2D Steady Newtonian Fluid Mechanics
\chapter{PINN Approximations to Navier-Stokes: Steady Newtonian Fluid Mechanics}
\input{chapter2.tex}
\subimport{notes/}{windkessel_overview.tex}
%\input{./notes/windkessel_overview.tex}
%\input{../notes/FOSLS/BLOCKSTENOSISSTEADY2D.tex}
%\input{/notes/FOSLS/BLOCKSTENOSISSTEADY2D.tex}
%\input{../notes/FOSLS/BLOCKSTENOSIS_STEADY_2D.tex}
%\input{../notes/FOSLS/SECTION_ANNULARRING_STEADY_2D.tex}
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% Chapter 
% 2D Steady Non-Newtonian Fluid Mechanics, Special Methods, Applications
\chapter{Chapter 2}
\input{chapter2.tex}
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% Chapter 
% Time-Dependent FOSLS Method, 1D/2D Advection-Diffusion-Reaction, Burger's, KdV, NL Schrodinger
\chapter{Chapter 2}
\input{chapter2.tex}
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% Chapter 
% PIGAN FOSLS vs Primitive FOSLS: Pressure Reconstruction, Darcy, and Elasticity
\chapter{Chapter 2}
\input{chapter2.tex}
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% Chapter 
% Bayesian PINNs vs Bayesian FOSLS PINNs for UQ, noise distributions
\chapter{Chapter 2}
\input{chapter2.tex}
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% Chapter 
% Operator Learning (DeepONet, MIONet, and Fourcastnet) 1D Deep LS, Deep FOSLS, Deep Energy Method comparison
\chapter{Chapter 2}
\input{chapter2.tex}
{\tiny }

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%% BIBLIOGRAPHY AND OTHER LISTS
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\backmatter

% Bibliography
\bibliography{dissertation}
\addtocontents{toc}{\protect\vspace*{\baselineskip}}

% Add bibliography to contents page
%\addcontentsline{toc}{chapter}{Bibliography} %'Bibliography' into toc

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%% APPENDICES
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\appendix
\chapter{}
\section{}

\end{document}