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updates for latex build

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NT 2021-04-04 13:48:21 +08:00
parent 2f6335f740
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24
diffphys-code-sol.ipynb
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@ -18,10 +18,10 @@
"\n", "\n",
"In order to learn the error function, we'll consider two different discretizations of the same PDE $\\mathcal P^*$: \n", "In order to learn the error function, we'll consider two different discretizations of the same PDE $\\mathcal P^*$: \n",
"a _reference_ version, which we assume to be accurate, with a discretized version \n", "a _reference_ version, which we assume to be accurate, with a discretized version \n",
"$\\mathcal P_r$, and solutions $\\mathbf r \\in \\mathscr R$, where $\\mathscr R$ denotes the manifold of solution of $\\mathcal P_r$.\n", "$\\mathcal P_r$, and solutions $\\mathbf r \\in \\mathscr R$, where $\\mathscr R$ denotes the manifold of solutions of $\\mathcal P_r$.\n",
"In parallel to this, we have a less accurate approximation of the same PDE, which we'll refer to as the _source_ version, as this will be the solver that our NN should later on interact with. Analogously,\n", "In parallel to this, we have a less accurate approximation of the same PDE, which we'll refer to as the _source_ version, as this will be the solver that our NN should later on interact with. Analogously,\n",
"we have $\\mathcal P_s$ with solutions $\\mathbf s \\in \\mathscr S$.\n", "we have $\\mathcal P_s$ with solutions $\\mathbf s \\in \\mathscr S$.\n",
"And after training, we'll have a _hybrid_ solver that uses $\\mathcal P_s$ in conjunction with a trained network to obtain improved solutions, i.e., solutions that are closer to the ones produced by $\\mathcal P_r$.\n", "After training, we'll obtain a _hybrid_ solver that uses $\\mathcal P_s$ in conjunction with a trained network to obtain improved solutions, i.e., solutions that are closer to the ones produced by $\\mathcal P_r$.\n",
"\n", "\n",
"```{figure} resources/diffphys-sol-manifolds.jpeg\n", "```{figure} resources/diffphys-sol-manifolds.jpeg\n",
"---\n", "---\n",
@ -39,7 +39,6 @@
}, },
"source": [ "source": [
"\n", "\n",
"explain coarse/ref setup...\n",
"Let's assume $\\mathcal{P}$ advances a solution by a time step $\\Delta t$, and let's denote $n$ consecutive steps by a superscript:\n", "Let's assume $\\mathcal{P}$ advances a solution by a time step $\\Delta t$, and let's denote $n$ consecutive steps by a superscript:\n",
"$\n", "$\n",
"\\newcommand{\\pde}{\\mathcal{P}}\n", "\\newcommand{\\pde}{\\mathcal{P}}\n",
@ -48,7 +47,7 @@
"\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n", "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
"\\newcommand{\\vcN}{\\vs} \n", "\\newcommand{\\vcN}{\\vs} \n",
"\\newcommand{\\project}{\\mathcal{T}} \n", "\\newcommand{\\project}{\\mathcal{T}} \n",
"\\vc{t+n} = \\pdec(\\pdec(\\cdots \\pdec( \\project \\vr{t} )\\cdots)) = \\pdec^n ( \\project \\vr{t} ) .\n", "\\vc{t+n} = \\pdec(\\pdec(\\cdots \\pdec( \\mathcal{T} \\vr{t} )\\cdots)) = \\pdec^n ( \\mathcal{T} \\vr{t} ) .\n",
"$\n", "$\n",
"Here we assume a mapping operator $\\mathcal{T}$ exists that transfers a reference solution to the source manifold. This could, e.g., be a simple downsampling operation.\n", "Here we assume a mapping operator $\\mathcal{T}$ exists that transfers a reference solution to the source manifold. This could, e.g., be a simple downsampling operation.\n",
"Especially for longer sequences, i.e. larger $n$, the source state \n", "Especially for longer sequences, i.e. larger $n$, the source state \n",
@ -62,17 +61,14 @@
"\\newcommand{\\corr}{\\mathcal{C}} \n", "\\newcommand{\\corr}{\\mathcal{C}} \n",
"\\newcommand{\\vc}[1]{\\mathbf{s}_{#1}} \n", "\\newcommand{\\vc}[1]{\\mathbf{s}_{#1}} \n",
"\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n", "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
"\\loss (\\vc{t},\\project \\vr{t})=\\Vert\\vc{t}-\\project \\vr{t}\\Vert_2$. \n", "\\loss (\\vc{t},\\mathcal{T} \\vr{t})=\\Vert\\vc{t}-\\mathcal{T} \\vr{t}\\Vert_2$. \n",
"Our learning goal is to train at a correction operator \n", "Our learning goal is to train at a correction operator \n",
"$\\newcommand{\\corr}{\\mathcal{C}} \n", "$\\mathcal{C} ( \\mathbf{s} )$ such that \n",
"\\corr ( \\vc{} )$ such that \n",
"a solution to which the correction is applied has a lower error than the original unmodified (source) \n", "a solution to which the correction is applied has a lower error than the original unmodified (source) \n",
"solution: $\\newcommand{\\loss}{e} \n", "solution: $\\newcommand{\\loss}{e} \n",
"\\newcommand{\\pdec}{\\pde_{s}}\n",
"\\newcommand{\\corr}{\\mathcal{C}} \n", "\\newcommand{\\corr}{\\mathcal{C}} \n",
"\\newcommand{\\project}{\\mathcal{T}} \n",
"\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n", "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
"\\loss ( \\pdec( \\corr (\\project \\vr{t_0}) ) , \\project \\vr{t_1}) < \\loss ( \\pdec( \\project \\vr{t_0} ), \\project \\vr{t_1})$. \n", "\\loss ( \\mathcal{P}_{s}( \\corr (\\mathcal{T} \\vr{t_0}) ) , \\mathcal{T} \\vr{t_1}) < \\loss ( \\mathcal{P}_{s}( \\mathcal{T} \\vr{t_0} ), \\mathcal{T} \\vr{t_1})$. \n",
"\n", "\n",
"The correction function \n", "The correction function \n",
"$\\newcommand{\\vcN}{\\mathbf{s}} \\newcommand{\\corr}{\\mathcal{C}} \\corr (\\vcN | \\theta)$ \n", "$\\newcommand{\\vcN}{\\mathbf{s}} \\newcommand{\\corr}{\\mathcal{C}} \\corr (\\vcN | \\theta)$ \n",
@ -82,11 +78,9 @@
"The overall learning goal now becomes\n", "The overall learning goal now becomes\n",
"\n", "\n",
"$\n", "$\n",
"\\newcommand{\\pdec}{\\pde_{s}}\n", "\\newcommand{\\corr}{\\mathcal{C}} \n",
"\\newcommand{\\corr}{\\mathcal{C}} \n",
"\\newcommand{\\project}{\\mathcal{T}} \n",
"\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n", "\\newcommand{\\vr}[1]{\\mathbf{r}_{#1}} \n",
"\\text{argmin}_\\theta | ( \\pdec \\corr )^n ( \\project \\vr{t} ) - \\project \\vr{t}|^2\n", "\\text{argmin}_\\theta | ( \\mathcal{P}_{s} \\corr )^n ( \\mathcal{T} \\vr{t} ) - \\mathcal{T} \\vr{t}|^2\n",
"$\n", "$\n",
"\n", "\n",
"A crucial bit here that's easy to overlook is that the correction depends on the modified states, i.e.\n", "A crucial bit here that's easy to overlook is that the correction depends on the modified states, i.e.\n",
@ -96,7 +90,7 @@
"These states actually evolve over time when training. They don't exist beforehand.\n", "These states actually evolve over time when training. They don't exist beforehand.\n",
"\n", "\n",
"**TL;DR**:\n", "**TL;DR**:\n",
"We'll train a network $\\mathcal{C}$ to reduce the numerical errors of a simulator with a more accurate reference. Here it's crucial to have the _source_ solver realized as a differential physics operator, such that it can give gradients for an improved training of $\\mathcal{C}$.\n", "We'll train a network $\\mathcal{C}$ to reduce the numerical errors of a simulator with a more accurate reference. It's crucial to have the _source_ solver realized as a differential physics operator, such that it can give gradients for an improved training of $\\mathcal{C}$.\n",
"\n", "\n",
"<br>\n", "<br>\n",
"\n", "\n",

37
make-pdf.sh Normal file
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@ -0,0 +1,37 @@
# source this file with "." in a shell
echo
echo Note: manually quit first latex pass with shift-x
echo
cd /Users/thuerey/Dropbox/mbaDevelSelected/pbdl-book/
/Users/thuerey/Library/Python/3.7/bin/jupyter-book build . --builder pdflatex
cd /Users/thuerey/Dropbox/mbaDevelSelected/pbdl-book/_build/latex
export JPYFILENAME=book.tex
rm ${JPYFILENAME}-in.bak
mv ${JPYFILENAME} ${JPYFILENAME}-in.bak
iconv -c -f utf-8 -t ascii ${JPYFILENAME}-in.bak > ${JPYFILENAME}
echo running SED
sed -i '' -e 's/sphinxincludegraphics{{/sphinxincludegraphics{/g' ${JPYFILENAME}
sed -i '' -e 's/}.png}/.png}/g' ${JPYFILENAME}
sed -i '' -e 's/}.jpg}/.jpg}/g' ${JPYFILENAME}
sed -i '' -e 's/}.jpeg}/.jpeg}/g' ${JPYFILENAME}
sed -i '' -e 's/sphinxpxdimen]{{/sphinxpxdimen]{/g' ${JPYFILENAME}
# ugly, -i doesnt work here:
sed '28i\
\\usepackage{mathrsfs} ' ${JPYFILENAME} > tmp-latex
echo renaming: tmp-latex ${JPYFILENAME}; ls -l tmp-latex ${JPYFILENAME}
rm ${JPYFILENAME}
mv tmp-latex ${JPYFILENAME}
echo running LATEX
pdflatex book
echo running LATEX , 2nd pass
pdflatex book
cd ../..