Online phase tutorial

.github/workflows/CI.yml

@@ -19,7 +19,6 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1.8'
           - '1.10'
           - '^1.11.0-0'
         os:

docs/make.jl

@@ -171,12 +171,19 @@ makedocs(;
             "BFGS Optimizer" => "optimizers/bfgs_optimizer.md",
             ],
         "Special Neural Network Layers" => [
-            "Sympnet Gradient Layers" => "layers/sympnet_gradient.md",
+            "Sympnet Layers" => "layers/sympnet_gradient.md",
             "Volume-Preserving Layers" => "layers/volume_preserving_feedforward.md",
             "Attention" => "layers/attention_layer.md",
             "Multihead Attention" => "layers/multihead_attention_layer.md",
             "Linear Symplectic Attention" => "layers/linear_symplectic_attention.md",
         ],
+        "Reduced Order Modelling" =>[
+            "General Framework" => "reduced_order_modeling/reduced_order_modeling.md",
+            "Network Losses" => "reduced_order_modeling/losses.md",
+            "PSD and Symplectic Autoencoders" => "reduced_order_modeling/symplectic_autoencoder.md",
+            "Kolmogorov n-width" => "reduced_order_modeling/kolmogorov_n_width.md",
+            "Projection and Reduction Error" => "reduced_order_modeling/projection_reduction_errors.md",
+        ],
         "Architectures" => [
             "Symplectic Autoencoders" => "architectures/symplectic_autoencoder.md",
             "Neural Network Integrators" => "architectures/neural_network_integrators.md",
@@ -190,12 +197,6 @@ makedocs(;
             "Routines" => "data_loader/data_loader.md",
             "Snapshot matrix & tensor" => "data_loader/snapshot_matrix.md",
         ],
-        "Reduced Order Modelling" =>[
-            "POD and Autoencoders" => "reduced_order_modeling/autoencoder.md",
-            "PSD and Symplectic Autoencoders" => "reduced_order_modeling/symplectic_autoencoder.md",
-            "Kolmogorov n-width" => "reduced_order_modeling/kolmogorov_n_width.md",
-            "Projection and Reduction Error" => "reduced_order_modeling/projection_reduction_errors.md",
-        ],
         "Tutorials" =>[
             "Sympnets" => "tutorials/sympnet_tutorial.md",
             "Symplectic Autoencoders" => "tutorials/symplectic_autoencoder.md",

docs/src/GeometricMachineLearning.bib

@@ -448,4 +448,14 @@ @inproceedings{huang2016riemannian
   pages={627--634},
   year={2016},
   organization={Springer}
+}
+
+@article{raissi2019physics,
+  title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
+  author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George E},
+  journal={Journal of Computational physics},
+  volume={378},
+  pages={686--707},
+  year={2019},
+  publisher={Elsevier}
 }

docs/src/architectures/symplectic_autoencoder.md

@@ -1,17 +1,75 @@
 # Symplectic Autoencoder 
 
+Symplectic autoencoders offer a structure-preserving way of mapping a high-dimensional system to a low dimensional system. Concretely this means that if we obtain a reduced system by means of a symplectic autoencoder, this system will again be reduced. 
+
+The architecture is represented by the figure below:
+
+```@example 
+Main.include_graphics("../tikz/symplectic_autoencoder") # hide
+```
+
+It is a composition of [SympNet gradient layers](@ref "SympNet Gradient Layer") and PSD-like matrices.
+
+
+## Intermediate Dimensions
+
+For a high-fidelity system of dimension ``2N`` and a reduced system of dimension ``2n``, the intermediate dimensions in the symplectic encoder and the decoder are computed according to: 
+
+```julia
+iterations = Vector{Int}(n : (N - n) ÷ (n_blocks - 1) : N)
+iterations[end] = full_dim2
+iterations * 2
+```
+
+So for e.g. ``2N = 100,`` ``2n = 10`` and ``\mathtt{n\_blocks} = 3`` we get 
+
+```math
+\mathrm{iterations} = 5\mathtt{:}(45 \div 2)\mathtt{:}50 = 5\mathtt{:}22\mathtt{:}50 = (5, 27, 49),
+```
+
+and after the further two modifications the dimensions are:
+
+```math
+(10, 54, 100).
+```
+
+
+## Example
+
 A visualization of an instance of [SymplecticAutoencoder](@ref) is shown below: 
 
 ```@example 
 Main.include_graphics("../tikz/symplectic_autoencoder_architecture") # 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`
+In this example shown in the figure `n_encoder_blocks` is two, `n_encoder_layers` is four, `n_decoder_blocks` is 3 and `n_decoder_layers` is 2. You can build such an instance of a symplectic autoencoder by calling:
+
+```@example sae
+using GeometricMachineLearning
+
+const full_dim = 100
+const reduced_dim = 10
+
+model = SymplecticAutoencoder(full_dim, reduced_dim; n_encoder_blocks = 2, n_encoder_layers = 4, n_decoder_blocks = 3, n_decoder_layers = 2)
+
+for layer in Chain(model)
+    println(stdout, layer)
+end
+```
+
+We also see that the intermediate dimension in the decoder is 54.
+
+## Library Functions
+
+```@docs; canonical = false
+SymplecticAutoencoder
+```
+
+## References
+
+```@bibliography
+Pages = []
+Canonical = false
 
-Note that all of these are keyword arguments that can be supplied to [SymplecticAutoencoder](@ref).
+brantner2023symplectic
+```