Documentation for v0.1 version (#199)

* Adding Equations, solving typos
* improve _code.rst
* the team rst and restuctore index.rst
* fixing errors

---------

Co-authored-by: Dario Coscia <dariocoscia@dhcp-015.eduroam.sissa.it>

docs/source/_rst/_code.rst

@@ -1,18 +1,85 @@
 Code Documentation
 ==================
 Welcome to PINA documentation! Here you can find the modules of the package divided in different sections.
+The high-level structure of the package is depicted in our API. 
+
+.. figure:: ../index_files/API_color.png
+    :alt: PINA application program interface
+    :align: center
+    :width: 400
+
+
+The pipeline to solve differential equations with PINA follows just five steps:
+
+    1. Define the `Problem`_ the user aim to solve
+    2. Generate data using built in `Geometries`_, or load high level simulation results as :doc:`LabelTensor <label_tensor>`
+    3. Choose or build one or more `Models`_ to solve the problem
+    4. Choose a solver across PINA available `Solvers`_, or build one using the :doc:`SolverInterface <solvers/solver_interface>`
+    5. Train the model with the PINA :doc:`Trainer <solvers/solver_interface>`, enhance the train with `Callbacks_`
 
 PINA Features
--------
+--------------
 .. toctree::
     :titlesonly:
 
     LabelTensor <label_tensor.rst>
     Condition <condition.rst>
+    Trainer <trainer.rst>
     Plotter <plotter.rst>
 
+
+Solvers
+--------------
+
+.. toctree::
+    :titlesonly:
+    
+    SolverInterface <solvers/solver_interface.rst>
+    PINN <solvers/pinn.rst>
+    Supervised solver <solvers/supervised.rst>
+    GAROM <solvers/garom.rst>
+
+
+Models
+------------
+
+.. toctree::
+    :titlesonly:
+    :maxdepth: 5
+
+    Network <models/network.rst>
+    FeedForward <models/fnn.rst>
+    MultiFeedForward <models/multifeedforward.rst>
+    ResidualFeedForward <models/fnn_residual.rst>
+    DeepONet <models/deeponet.rst>
+    MIONet <models/mionet.rst>
+    FNO <models/fno.rst>
+
+Layers
+-------------
+
+.. toctree::
+    :titlesonly:
+
+    Residual layer <layers/residual.rst>
+    EnhancedLinear layer <layers/enhanced_linear.rst>
+    Spectral convolution <layers/spectral.rst>
+    Fourier layers <layers/fourier.rst>
+    Continuous convolution <layers/convolution.rst>
+    
+
+Equations and Operators
+-------------------------
+
+.. toctree::
+    :titlesonly:
+    
+    Equations <equations.rst>
+    Differential Operators <operators.rst>
+
+
 Problem
--------
+--------------
 
 .. toctree::
     :titlesonly:
@@ -22,40 +89,8 @@ Problem
     TimeDependentProblem <problem/timedepproblem.rst>
     ParametricProblem <problem/parametricproblem.rst>
 
-Solvers
--------
-
-.. toctree::
-    :titlesonly:
-    
-    SolverInterface <solvers/solver_interface.rst>
-    PINN <solvers/pinn.rst>
-
-
-Models
------
-
-.. toctree::
-    :titlesonly:
-
-    Network <models/network.rst>
-    FeedForward <models/fnn.rst>
-    MultiFeedForward <models/multifeedforward.rst>
-    ResidualFeedForward <models/fnn_residual.rst>
-    DeepONet <models/deeponet.rst>
-    FNO <models/fno.rst>
-
-Layers
-------
-
-.. toctree::
-    :titlesonly:
-
-    ContinuousConv <layers/convolution.rst>
-    
-
 Geometries
-----------
+-----------------
 
 .. toctree::
     :titlesonly:
@@ -65,9 +100,30 @@ Geometries
     EllipsoidDomain <geometry/ellipsoid.rst>
     SimplexDomain <geometry/simplex.rst>
 
+Geometry set operations
+------------------------
 
-Loss
-------
+.. toctree::
+    :titlesonly:
+
+    OperationInterface <geometry/operation_interface.rst>
+    Union <geometry/union_domain.rst>
+    Intersection <geometry/intersection_domain.rst>
+    Difference <geometry/difference_domain.rst>
+    Exclusion <geometry/exclusion_domain.rst>
+
+Callbacks
+--------------------
+
+.. toctree::
+    :titlesonly:
+
+    Metric tracking <callbacks/processing_callbacks.rst>
+    Optimizer callbacks <callbacks/optimizer_callbacks.rst>
+    Adaptive Refinments <callbacks/adaptive_refinment_callbacks.rst>
+
+Metrics and Losses
+--------------------
 
 .. toctree::
     :titlesonly: