peci1 · November 15, 2024 18:13
diff --git a/ballistic_curve.ipynb b/ballistic_curve.ipynb
diff --git a/ballistic_curve.tex b/ballistic_curve.tex
 \documentclass{beamer}

 \usepackage{listings}
 \lstset{language={[LaTeX]TeX}, basicstyle=\small}

 \usepackage{multimedia}

 \definecolor{links}{HTML}{302080}
 \hypersetup{colorlinks,linkcolor=links,urlcolor=links}

 \usepackage[utf8]{inputenc}
 \usepackage{xspace}

 \usetheme{Madrid}

 \usepackage[overridenote]{pdfpc}

 \mode<presentation>

 \title[Physical Intuition in DNNs]{Physical Intuition in Deep Neural Networks}
 \author[Martin Pecka]{Martin Pecka}
 \institute[CTU FEE]{Czech Technical University in Prague, Faculty of Electrical Engineering}

 \begin{document}

 \begin{frame}{PINN: Example: Ballistic Curve}
 	\begin{center}
 		The curve is defined by a differential equation and initial conditions:
 		$$\vec{a} = -\mu \|\vec{v}\| \vec{v} - \vec{g}$$
 		$$\mu = 0.03; \vec{s_0} = (0, 0); \vec{v_0} = (200, 200) $$
 		\includegraphics[width=\linewidth]{gt.png}
 	\end{center}
 \end{frame}


 \begin{frame}{PINN: Example: Ballistic Curve}
 	\begin{center}
 		There is no closed-form solution for $\vec{s_t}$, numerical integration is needed.\\
 		\includegraphics[width=\linewidth]{gt.png}
 	\end{center}
 \end{frame}

 \begin{frame}{PINN: Example: Ballistic Curve: Black-box NN}
 	\begin{center}
 		$$ \texttt{loss} = \|\hat{\vec{s}} - \vec{s_{train}} \|^2 $$
 		\href{run:train-dumb.mp4?autostart&loop}
 		{\includegraphics[width=\linewidth]{train-dumb.png}}
 	\end{center}
 \end{frame}


 \begin{frame}{PINN: Example: Ballistic Curve: Black-box NN with L2 Regularizer}
 	\begin{center}
 		$$ \texttt{loss} = \|\hat{\vec{s}} - \vec{s_{train}} \|^2 + \sum \| \vec{w} \|^2 $$
 		\href{run:train-l2.mp4?autostart&loop}
 		{\includegraphics[width=\linewidth]{train-l2.png}}
 	\end{center}
 \end{frame}

 \begin{frame}{PINN: Example: Ballistic Curve: Gray-box NN}
 	\begin{center}
    Add the error in the differential equation to the loss. $\vec{v}$ an $\vec{a}$ are actually already computed by the net - they are the gradients (and 2nd order gradients).
 		$$ \texttt{loss} = \|\hat{\vec{s}} - \vec{s_{train}} \|^2 + \sum \| \vec{a} - (-\mu \|\vec{v}\| \vec{v} - \vec{g}) \|^2 $$
 		\href{run:train-pinn.mp4?autostart&loop}
 		{\includegraphics[width=\linewidth]{train-pinn.png}}
 	\end{center}
 \end{frame}

 \end{document}
diff --git a/gt.png b/gt.png
diff --git a/pdfpc.sty b/pdfpc.sty
 %  This file is part of pdfpc.
 %  Copyright (C) 2023 Evgeny Stambulchik
 %
 %  This program is free software; you can redistribute it and/or modify
 %  it under the terms of the GNU General Public License as published by
 %  the Free Software Foundation; either version 3 of the License, or
 %  (at your option) any later version.
 %
 %  This program is distributed in the hope that it will be useful,
 %  but WITHOUT ANY WARRANTY; without even the implied warranty of
 %  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 %  GNU General Public License for more details.
 %
 %  You should have received a copy of the GNU General Public License along
 %  with this program; if not, write to the Free Software Foundation, Inc.,
 %  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
 %  -------------------------------------------------------------------------------------------
 %
 %  Allow for defining some meta data and simple textual notes for use
 %  with the pdfpc presentation application <https://pdfpc.github.io>.
 %
 %  -------------------------------------------------------------------------------------------
 %
 %  Inspired by Carsten Brandt's <https://github.com/cebe/pdfpc-latex-notes>.
 %
 %  -------------------------------------------------------------------------------------------
 %
 %  Please report bugs and other problems as well as suggestions for improvements
 %  to the issue tracker at github <https://github.com/pdfpc/pdfpc/>
 %
 %  -------------------------------------------------------------------------------------------
 %
 \ProvidesPackage{pdfpc}[2023/10/21 v0.7.1 PDFPC]
 \NeedsTeXFormat{LaTeX2e}
 %
 % Require additional packages needed by \sty{pdfpc}:
 \RequirePackage{kvoptions}
 \RequirePackage{xstring}
 \RequirePackage{iftex}
 \RequirePackage{hyperxmp}
 \ifLuaTeX
  \RequirePackage{stringenc}
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  prefix=PDFPC@
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 \DeclareStringOption{starttime}
 \DeclareStringOption{endtime}
 \DeclareStringOption{enduserslide}
 \DeclareStringOption{lastminutes}
 \DeclareBoolOption{hidenotes}
 \DeclareBoolOption{overridenote}
 \DeclareStringOption{notesposition}
 \DeclareBoolOption[false]{disablemarkdown}
 \DeclareStringOption{defaulttransition}
 \DeclareDefaultOption{\@unknownoptionerror}
 %
 \ProcessKeyvalOptions*
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 \ifx\PDFPC@duration\@empty
 \else
  \IfInteger{\PDFPC@duration}{}
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 \fi
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  }%
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diff --git a/train-dumb.gif b/train-dumb.gif
diff --git a/train-dumb.mp4 b/train-dumb.mp4
diff --git a/train-dumb.png b/train-dumb.png
diff --git a/train-l2.gif b/train-l2.gif
diff --git a/train-l2.mp4 b/train-l2.mp4
diff --git a/train-l2.png b/train-l2.png
diff --git a/train-pinn.gif b/train-pinn.gif
diff --git a/train-pinn.mp4 b/train-pinn.mp4
diff --git a/train-pinn.png b/train-pinn.png
	\documentclass{beamer}

	\usepackage{listings}
	\lstset{language={[LaTeX]TeX}, basicstyle=\small}

	\usepackage{multimedia}

	\definecolor{links}{HTML}{302080}
	\hypersetup{colorlinks,linkcolor=links,urlcolor=links}

	\usepackage[utf8]{inputenc}
	\usepackage{xspace}

	\usetheme{Madrid}

	\usepackage[overridenote]{pdfpc}

	\mode<presentation>

	\title[Physical Intuition in DNNs]{Physical Intuition in Deep Neural Networks}
	\author[Martin Pecka]{Martin Pecka}
	\institute[CTU FEE]{Czech Technical University in Prague, Faculty of Electrical Engineering}

	\begin{document}

	\begin{frame}{PINN: Example: Ballistic Curve}
	\begin{center}
	The curve is defined by a differential equation and initial conditions:
	$$\vec{a} = -\mu \\|\vec{v}\\| \vec{v} - \vec{g}$$
	$$\mu = 0.03; \vec{s_0} = (0, 0); \vec{v_0} = (200, 200) $$
	\includegraphics[width=\linewidth]{gt.png}
	\end{center}
	\end{frame}


	\begin{frame}{PINN: Example: Ballistic Curve}
	\begin{center}
	There is no closed-form solution for $\vec{s_t}$, numerical integration is needed.\\
	\includegraphics[width=\linewidth]{gt.png}
	\end{center}
	\end{frame}

	\begin{frame}{PINN: Example: Ballistic Curve: Black-box NN}
	\begin{center}
	$$ \texttt{loss} = \\|\hat{\vec{s}} - \vec{s_{train}} \\|^2 $$
	\href{run:train-dumb.mp4?autostart&loop}
	{\includegraphics[width=\linewidth]{train-dumb.png}}
	\end{center}
	\end{frame}


	\begin{frame}{PINN: Example: Ballistic Curve: Black-box NN with L2 Regularizer}
	\begin{center}
	$$ \texttt{loss} = \\|\hat{\vec{s}} - \vec{s_{train}} \\|^2 + \sum \\| \vec{w} \\|^2 $$
	\href{run:train-l2.mp4?autostart&loop}
	{\includegraphics[width=\linewidth]{train-l2.png}}
	\end{center}
	\end{frame}

	\begin{frame}{PINN: Example: Ballistic Curve: Gray-box NN}
	\begin{center}
	Add the error in the differential equation to the loss. $\vec{v}$ an $\vec{a}$ are actually already computed by the net - they are the gradients (and 2nd order gradients).
	$$ \texttt{loss} = \\|\hat{\vec{s}} - \vec{s_{train}} \\|^2 + \sum \\| \vec{a} - (-\mu \\|\vec{v}\\| \vec{v} - \vec{g}) \\|^2 $$
	\href{run:train-pinn.mp4?autostart&loop}
	{\includegraphics[width=\linewidth]{train-pinn.png}}
	\end{center}
	\end{frame}

	\end{document}
	% This file is part of pdfpc.
	% Copyright (C) 2023 Evgeny Stambulchik
	%
	% This program is free software; you can redistribute it and/or modify
	% it under the terms of the GNU General Public License as published by
	% the Free Software Foundation; either version 3 of the License, or
	% (at your option) any later version.
	%
	% This program is distributed in the hope that it will be useful,
	% but WITHOUT ANY WARRANTY; without even the implied warranty of
	% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	% GNU General Public License for more details.
	%
	% You should have received a copy of the GNU General Public License along
	% with this program; if not, write to the Free Software Foundation, Inc.,
	% 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
	% -------------------------------------------------------------------------------------------
	%
	% Allow for defining some meta data and simple textual notes for use
	% with the pdfpc presentation application <https://pdfpc.github.io>.
	%
	% -------------------------------------------------------------------------------------------
	%
	% Inspired by Carsten Brandt's <https://github.com/cebe/pdfpc-latex-notes>.
	%
	% -------------------------------------------------------------------------------------------
	%
	% Please report bugs and other problems as well as suggestions for improvements
	% to the issue tracker at github <https://github.com/pdfpc/pdfpc/>
	%
	% -------------------------------------------------------------------------------------------
	%
	\ProvidesPackage{pdfpc}[2023/10/21 v0.7.1 PDFPC]
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