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ch-PINN.tex
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ch-PINN.tex
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\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage[version=4]{mhchem}
\usepackage{stmaryrd}
\usepackage{graphicx}
\usepackage[export]{adjustbox}
\graphicspath{ {./images/} }
\usepackage{mathrsfs}
\usepackage{bbold}
\usepackage{multirow}
\newcommand{\thmsymbol}{\( \diamond \)}
\newtheorem{remarkex}{Remark}
\newenvironment{remark}
{\pushQED{\qed}\renewcommand{\qedsymbol}{$\triangle$}\remarkex}
{\popQED\endremarkex}
\newtheorem{definitionex}{Definition}
\newenvironment{definition}
{\pushQED{\qed}\renewcommand{\qedsymbol}{$\star$}\definitionex}
{\popQED\enddefinitionex}
\newtheorem{assumptionex}{Assumption}
\newenvironment{assumption}
{\pushQED{\qed}\renewcommand{\qedsymbol}{$\bullet$}\assumptionex}
{\popQED\endassumptionex}
%
%\title{PINN Overview}
%\author{Charles Talbot}
%\date{May 2023}
%
\begin{document}
%
%\maketitle
\section{Physics Informed Neural Networks}
%
\input{ch-PINNModulus.tex}
%
\input{slide-UseCasePINNs.tex}
%
\input{ch-Methods.tex}
%
\input{slide--PINNConvergence.tex}
%
\input{sec-ModulusPDEStandards.tex}
% Empty
\input{ch-NeuralTangentKernel.tex}
%
\input{sec-PINNsAdvancedTechniques.tex}
%
\input{sec-PINN-PDESolution-WeakForm.tex}
% \input{ref-PINNConvergence.tex}
\input{PINNConvergence.tex}
%\include{sec-PINN-PDESolution-WeakForm.tex
%
%\begin{definition}{\normalfont (Fully-Connected Feed-Forward Neural Network)}
% {\normalfont
% blah2}
%\end{definition}
%\begin{remark}{\normalfont (blah1)}
% {\normalfont
% blah2}
%\end{remark}
%
%\begin{assumption}{\normalfont (blah1)}
% {\normalfont
% blah2}
%\end{assumption}
%\externalfigure[https://cdn.mathpix.com/cropped/2022_12_28_695a9767d794b8ad368eg-027.jpg?height=391&width=1575&top_left_y=230&top_left_x=275]
%\externalfigure["https://cdn.mathpix.com/cropped/2022_12_28_695a9767d794b8ad368eg-027.jpg"]
%
%\begin{figure}
% \href{http://commons.wikimedia.org/wiki/File:Pachydyptes_ponderosus.jpg}{\includegraphics[width=\textwidth]}
%% {picture}}
%% \includegraphics[width=\textwidth]
%% \href{https://cdn.mathpix.com/cropped/2022_12_28_695a9767d794b8ad368eg-027.jpg}
%% \caption{A reconstruction of New Zealand Giant Penguins (\emph{pachydyptes ponderosus}) by
%% F.~W.~Kuhnert (1865--1926). Click on the image to visit the page on Wikimedia Commons where it
%% was downloaded from.}
%\end{figure}
\end{document}