Updated ReducedSystem and renamed to HRedSys (including tutorial)

Project.toml

@@ -11,9 +11,11 @@ ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
 Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 GeometricBase = "9a0b12b7-583b-4f04-aa1f-d8551b6addc9"
 GeometricEquations = "c85262ba-a08a-430a-b926-d29770767bf2"
 GeometricIntegrators = "dcce2d33-59f6-5b8d-9047-0defad88ae06"
+GeometricSolutions = "7843afe4-64f4-4df4-9231-049495c56661"
 HDF5 = "f67ccb44-e63f-5c2f-98bd-6dc0ccc4ba2f"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
@@ -52,6 +54,7 @@ julia = "1.8"
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
+FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 GeometricEquations = "c85262ba-a08a-430a-b926-d29770767bf2"
 GeometricProblems = "18cb22b4-ad41-5c80-9c5f-710df63fbdc9"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -60,4 +63,4 @@ SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["ChainRulesTestUtils", "Random", "SafeTestsets", "Test"]
+test = ["ChainRulesTestUtils", "Random", "SafeTestsets", "Test", "GeometricProblems", "FiniteDifferences"]

docs/Project.toml

@@ -10,6 +10,7 @@ GeometricBase = "9a0b12b7-583b-4f04-aa1f-d8551b6addc9"
 GeometricEquations = "c85262ba-a08a-430a-b926-d29770767bf2"
 GeometricIntegrators = "dcce2d33-59f6-5b8d-9047-0defad88ae06"
 GeometricMachineLearning = "194d25b2-d3f5-49f0-af24-c124f4aa80cc"
+GeometricProblems = "18cb22b4-ad41-5c80-9c5f-710df63fbdc9"
 Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 KernelAbstractions = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
@@ -19,4 +20,4 @@ Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
-Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"

docs/make.jl

@@ -43,6 +43,7 @@ makedocs(;
         "Home" => "index.md",
         "Architectures" => [
             "SympNet" => "architectures/sympnet.md",
+            "Symplectic Autoencoders" => "architectures/symplectic_autoencoder.md",
         ],
         "Manifolds" => [
             "Concepts from General Topology" => "manifolds/basic_topology.md",
@@ -90,7 +91,7 @@ makedocs(;
         ],
         "Tutorials" =>[
             "Sympnets" => "tutorials/sympnet_tutorial.md",
-            "Linear Wave Equation" => "tutorials/linear_wave_equation.md",
+            "Symplectic Autoencoders" => "tutorials/symplectic_autoencoder.md",
             "MNIST" => "tutorials/mnist_tutorial.md",
             "Grassmann manifold" => "tutorials/grassmann_layer.md",
             "Volume-Preserving Attention" => "tutorials/volume_preserving_attention.md",

docs/src/architectures/symplectic_autoencoder.md

@@ -0,0 +1,28 @@
+# Symplectic Autoencoder 
+
+A visualization of an instance of [SymplecticAutoencoder](@ref) is shown below: 
+
+```@example
+import Images, Plots # hide
+if Main.output_type == :html # hide
+  HTML("""<object type="image/svg+xml" class="display-light-only" data=$(joinpath(Main.buildpath, "../tikz/symplectic_autoencoder_architecture.png"))></object>""") # hide
+else # hide
+  Plots.plot(Images.load("../tikz/symplectic_autoencoder_architecture.png"), axis=([], false)) # hide
+end # hide
+```
+
+```@example
+if Main.output_type == :html # hide
+  HTML("""<object type="image/svg+xml" class="display-dark-only" data=$(joinpath(Main.buildpath, "../tikz/symplectic_autoencoder_architecture_dark.png"))></object>""") # hide
+end # hide
+```
+
+The *intermediate dimension* ``M`` is calculated via `n : (N - n) ÷ (n_blocks - 1) : N`. Further we have the following choices:
+- `n_encoder_layers::Integer = 4`
+- `n_encoder_blocks::Integer = 2` 
+- `n_decoder_layers::Integer = 2` 
+- `n_decoder_blocks::Integer = 3`
+- `encoder_init_q::Bool = true`
+- `decoder_init_q::Bool = true`
+
+Note that all of these are keyword arguments that can be supplied to [SymplecticAutoencoder](@ref).

docs/src/tikz/Makefile

@@ -39,6 +39,8 @@ png:
 	pdftocairo 	-png -r $(res1) -transp -singlefile	 logo.pdf										logo 
 	pdftocairo  -png -r $(res1) -transp -singlefile  symplectic_autoencoder.pdf						symplectic_autoencoder
 	pdftocairo  -png -r $(res1) -transp -singlefile  symplectic_autoencoder_dark.pdf				symplectic_autoencoder_dark
+	pdftocairo  -png -r $(res1) -transp -singlefile  symplectic_autoencoder_architecture.pdf		symplectic_autoencoder_architecture
+	pdftocairo  -png -r $(res1) -transp -singlefile  symplectic_autoencoder_architecture_dark.pdf	symplectic_autoencoder_architecture_dark
 	pdftocairo  -png -r $(res1) -transp -singlefile  solution_manifold_2.pdf						solution_manifold_2
 	pdftocairo  -png -r $(res1) -transp -singlefile  mha.pdf 										mha
 	pdftocairo  -png -r $(res1) -transp -singlefile  mha_dark.pdf 									mha_dark

docs/src/tikz/symplectic_autoencoder_architecture.tex

@@ -0,0 +1,69 @@
+\documentclass[crop, tikz]{standalone}
+
+\usepackage{tikz}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage[mode=buildnew]{standalone}
+
+\usepackage{xcolor}
+
+
+\usetikzlibrary{positioning}
+\usetikzlibrary{calc}
+\usetikzlibrary{fit}
+%\usepackage{nicematrix}
+
+\tikzset{set/.style={draw,circle,inner sep=0pt,align=center}}
+
+\definecolor{morange}{RGB}{255,127,14}
+\definecolor{mblue}{RGB}{31,119,180}
+\definecolor{mred}{RGB}{214,39,40}
+\definecolor{mpurple}{RGB}{148,103,189}
+\definecolor{mgreen}{RGB}{44,160,44}
+
+
+\begin{document}
+\begin{tikzpicture}[module/.style={draw, very thick, rounded corners, minimum width=15ex},
+    gradient/.style={module, fill=mgreen!50},
+    psd/.style={module, fill=mblue!50},
+    arrow/.style={-stealth, thick, rounded corners},
+]
+\node (input) {Input};
+\node[above of=input, gradient, align=center, yshift=.6cm] (gq1) {\texttt{GradientQ(2N, 10N, tanh)}};
+\node[above of=gq1, gradient, align=center] (gq2) {\texttt{GradientP(2N, 10N, tanh)}};
+\node[above of=gq2, gradient, align=center] (gq3) {\texttt{GradientQ(2N, 10N, tanh)}};
+\node[above of=gq3, gradient, align=center] (gq4) {\texttt{GradientP(2N, 10N, tanh)}};
+\node[above of=gq4, psd, align=center] (psd1) {\texttt{PSDLayer(2N, 2n)}};
+
+\node[right of=input, xshift=6cm] (output) {Output}; 
+\node[above of=output, psd] (psd3) {\texttt{PSDLayer(2M, 2N)}};
+\node[above of=psd3, gradient] (gq8) {\texttt{GradientP(2M, 2M, tanh)}};
+\node[above of=gq8, gradient] (gq7) {\texttt{GradientQ(2M, 2M, tanh)}};
+\node[above of=gq7, psd] (psd2) {\texttt{PSDLayer(2n, 2M)}};
+\node[above of=psd2, gradient] (gq6) {\texttt{GradientP(2n, 10n, tanh)}};
+\node[above of=gq6, gradient] (gq5) {\texttt{GradientQ(2n, 10n, tanh)}};
+
+\draw[arrow] (gq1) -- (gq2);
+\draw[arrow] (gq2) -- (gq3); 
+\draw[arrow] (gq3) -- (gq4);
+\draw[arrow] (gq4) -- (psd1); 
+
+\coordinate[above of=gq5] (gq5_above);
+\coordinate[left of=gq5_above, xshift=-6cm] (psd_above);
+
+\draw[arrow] (gq5) -- (gq6);
+\draw[arrow] (gq6) -- (psd2);
+\draw[arrow] (psd2) -- (gq7);
+\draw[arrow] (gq7) -- (gq8);
+\draw[arrow] (gq8) -- (psd3);
+
+\node[fit=(gq1)(gq2)(gq3)(gq4)(psd1),draw, ultra thick, rounded corners, label=left:$\Psi^e$] (encoder) {};
+\node[fit=(gq5)(gq5)(gq7)(psd2)(gq7)(gq8)(psd3),draw, ultra thick, rounded corners, label=left:$\Psi^d$] (decoder) {};
+
+\draw[arrow] (encoder.north)-|(psd_above)-|(gq5_above)--(decoder.north);
+\draw[arrow] (input) -- (encoder);
+\draw[arrow] (decoder) -- (output);
+
+
+\end{tikzpicture}
+\end{document}

docs/src/tikz/symplectic_autoencoder_architecture_dark.tex

@@ -0,0 +1,69 @@
+\documentclass[crop, tikz]{standalone}
+
+\usepackage{tikz}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage[mode=buildnew]{standalone}
+
+\usepackage{xcolor}
+
+
+\usetikzlibrary{positioning}
+\usetikzlibrary{calc}
+\usetikzlibrary{fit}
+%\usepackage{nicematrix}
+
+\tikzset{set/.style={draw,circle,inner sep=0pt,align=center}}
+
+\definecolor{morange}{RGB}{255,127,14}
+\definecolor{mblue}{RGB}{31,119,180}
+\definecolor{mred}{RGB}{214,39,40}
+\definecolor{mpurple}{RGB}{148,103,189}
+\definecolor{mgreen}{RGB}{44,160,44}
+
+
+\begin{document}
+\begin{tikzpicture}[module/.style={draw, very thick, rounded corners, minimum width=15ex},
+    gradient/.style={module, fill=mgreen!50},
+    psd/.style={module, fill=mblue!50},
+    arrow/.style={-stealth, thick, rounded corners},
+]
+\node (input) {\color{white} Input};
+\node[above of=input, gradient, align=center, yshift=.6cm] (gq1) {\texttt{GradientQ(2N, 10N, tanh)}};
+\node[above of=gq1, gradient, align=center] (gq2) {\texttt{GradientP(2N, 10N, tanh)}};
+\node[above of=gq2, gradient, align=center] (gq3) {\texttt{GradientQ(2N, 10N, tanh)}};
+\node[above of=gq3, gradient, align=center] (gq4) {\texttt{GradientP(2N, 10N, tanh)}};
+\node[above of=gq4, psd, align=center] (psd1) {\texttt{PSDLayer(2N, 2n)}};
+
+\node[right of=input, xshift=6cm] (output) {\color{white} Output}; 
+\node[above of=output, psd] (psd3) {\texttt{PSDLayer(2M, 2N)}};
+\node[above of=psd3, gradient] (gq8) {\texttt{GradientP(2M, 2M, tanh)}};
+\node[above of=gq8, gradient] (gq7) {\texttt{GradientQ(2M, 2M, tanh)}};
+\node[above of=gq7, psd] (psd2) {\texttt{PSDLayer(2n, 2M)}};
+\node[above of=psd2, gradient] (gq6) {\texttt{GradientP(2n, 10n, tanh)}};
+\node[above of=gq6, gradient] (gq5) {\texttt{GradientQ(2n, 10n, tanh)}};
+
+\draw[arrow, color=white] (gq1) -- (gq2);
+\draw[arrow, color=white] (gq2) -- (gq3); 
+\draw[arrow, color=white] (gq3) -- (gq4);
+\draw[arrow, color=white] (gq4) -- (psd1); 
+
+\coordinate[above of=gq5] (gq5_above);
+\coordinate[left of=gq5_above, xshift=-6cm] (psd_above);
+
+\draw[arrow, color=white] (gq5) -- (gq6);
+\draw[arrow, color=white] (gq6) -- (psd2);
+\draw[arrow, color=white] (psd2) -- (gq7);
+\draw[arrow, color=white] (gq7) -- (gq8);
+\draw[arrow, color=white] (gq8) -- (psd3);
+
+\node[fit=(gq1)(gq2)(gq3)(gq4)(psd1),draw, ultra thick, rounded corners, color=white, label=left:\color{white}$\Psi^e$] (encoder) {};
+\node[fit=(gq5)(gq5)(gq7)(psd2)(gq7)(gq8)(psd3),draw, ultra thick, rounded corners, color=white, label=left:\color{white}$\Psi^d$] (decoder) {};
+
+\draw[arrow, color=white] (encoder.north)-|(psd_above)-|(gq5_above)--(decoder.north);
+\draw[arrow, color=white] (input) -- (encoder);
+\draw[arrow, color=white] (decoder) -- (output);
+
+
+\end{tikzpicture}
+\end{document}