Update Tutorials (#544)

* update tutorials
* tutorial guidelines
* doc

tutorials/README.md

@@ -1,36 +1,47 @@
-# PINA Tutorials
+# 🚀 Welcome to the PINA Tutorials!
+
+In this folder we collect useful tutorials in order to understand the principles and the potential of **PINA**. Whether you're just getting started or looking to deepen your understanding, these resources are here to guide you.
+
+The table below provides an overview of each tutorial. All tutorials are also available in HTML in the official [PINA documentation](http://mathlab.github.io/PINA/).
 
-In this folder we collect useful tutorials in order to understand the principles and the potential of **PINA**. Please read the following table for details about the tutorials. The HTML version of all the tutorials is available also within the [documentation](http://mathlab.github.io/PINA/).
 
 ## Getting started with PINA
 
 | Description   | Tutorial |
 |---------------|-----------|
-Introduction to PINA for Physics Informed Neural Networks training|[[.ipynb](tutorial1/tutorial.ipynb), [.py](tutorial1/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial1/tutorial.html)]|
-Introduction to PINA `Equation` class|[[.ipynb](tutorial12/tutorial.ipynb), [.py](tutorial12/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial12/tutorial.html)]|
-PINA and PyTorch Lightning, training tips and visualizations|[[.ipynb](tutorial11/tutorial.ipynb), [.py](tutorial11/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial11/tutorial.html)]|
-Building custom geometries with PINA `Location` class|[[.ipynb](tutorial6/tutorial.ipynb), [.py](tutorial6/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial6/tutorial.html)]|
+Introductory Tutorial: A Beginner’s Guide to PINA|[[.ipynb](tutorial17/tutorial.ipynb),[.py](tutorial17/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial17/tutorial.html)]|
+How to build a `Problem` in PINA|[[.ipynb](tutorial16/tutorial.ipynb),[.py](tutorial16/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial16/tutorial.html)]|
+Introduction to Solver classes|[[.ipynb](tutorial18/tutorial.ipynb),[.py](tutorial18/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial18/tutorial.html)]|
+Introduction to `Trainer` class|[[.ipynb](tutorial11/tutorial.ipynb),[.py](tutorial11/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial11/tutorial.html)]|
+Data structure for SciML: `Tensor`, `LabelTensor`, `Data` and `Graph` |[[.ipynb](tutorial19/tutorial.ipynb),[.py](tutorial19/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial19/tutorial.html)]|
+Building geometries with `DomainInterface` class|[[.ipynb](tutorial6/tutorial.ipynb),[.py](tutorial6/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial6/tutorial.html)]|
+Introduction to PINA `Equation` class|[[.ipynb](tutorial12/tutorial.ipynb),[.py](tutorial12/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial12/tutorial.html)]|
 
 
 ## Physics Informed Neural Networks
 | Description   | Tutorial  |
 |---------------|-----------|
-Two dimensional Poisson problem using Extra Features Learning     |[[.ipynb](tutorial2/tutorial.ipynb), [.py](tutorial2/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial2/tutorial.html)]|
-Two dimensional Wave problem with hard constraint |[[.ipynb](tutorial3/tutorial.ipynb), [.py](tutorial3/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial3/tutorial.html)]|
-Resolution of a 2D Poisson inverse problem |[[.ipynb](tutorial7/tutorial.ipynb), [.py](tutorial7/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial7/tutorial.html)]|
-Periodic Boundary Conditions for Helmotz Equation |[[.ipynb](tutorial9/tutorial.ipynb), [.py](tutorial9/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial9/tutorial.html)]|
-Multiscale PDE learning with Fourier Feature Network |[[.ipynb](tutorial13/tutorial.ipynb), [.py](tutorial13/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial13/tutorial.html)]|
+Introductory Tutorial:  Physics Informed Neural Networks with PINA |[[.ipynb](tutorial1/tutorial.ipynb),[.py](tutorial1/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial1/tutorial.html)]|
+Enhancing PINNs with Extra Features to solve the Poisson Problem |[[.ipynb](tutorial2/tutorial.ipynb),[.py](tutorial2/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial2/tutorial.html)]|
+Applying Hard Constraints in PINNs to solve the Wave Problem |[[.ipynb](tutorial3/tutorial.ipynb),[.py](tutorial3/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial3/tutorial.html)]|
+Applying Periodic Boundary Conditions in PINNs to solve the Helmotz Problem |[[.ipynb](tutorial9/tutorial.ipynb),[.py](tutorial9/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial9/tutorial.html)]|
+Inverse Problem Solving with Physics-Informed Neural Network |[[.ipynb](tutorial7/tutorial.ipynb),[.py](tutorial7/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial7/tutorial.html)]|
+Learning Multiscale PDEs Using Fourier Feature Networks|[[.ipynb](tutorial13/tutorial.ipynb),[.py](tutorial13/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial13/tutorial.html)]|
+Learning Bifurcating PDE Solutions with Physics-Informed Deep Ensembles|[[.ipynb](tutorial14/tutorial.ipynb),[.py](tutorial14/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial14/tutorial.html)]|
 
 
 ## Neural Operator Learning
 | Description   | Tutorial  |
 |---------------|-----------|
-Two dimensional Darcy flow using the Fourier Neural Operator          |[[.ipynb](tutorial5/tutorial.ipynb), [.py](tutorial5/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial5/tutorial.html)]|
-Time dependent Kuramoto Sivashinsky equation using the Averaging Neural Operator          |[[.ipynb](tutorial10/tutorial.ipynb), [.py](tutorial10/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial10/tutorial.html)]|
+Introductory Tutorial: Neural Operator Learning with PINA |[[.ipynb](tutorial21/tutorial.ipynb),[.py](tutorial21/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial21/tutorial.html)]|
+Modeling 2D Darcy Flow with the Fourier Neural Operator |[[.ipynb](tutorial5/tutorial.ipynb),[.py](tutorial5/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial5/tutorial.html)]|
+Solving the Kuramoto–Sivashinsky Equation with Averaging Neural Operator |[[.ipynb](tutorial10/tutorial.ipynb),[.py](tutorial10/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial10/tutorial.html)]|
 
 ## Supervised Learning
 | Description   | Tutorial  |
 |---------------|-----------|
-Unstructured convolutional autoencoder via continuous convolution |[[.ipynb](tutorial4/tutorial.ipynb), [.py](tutorial4/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial4/tutorial.html)]|
-POD-RBF and POD-NN for reduced order modeling| [[.ipynb](tutorial8/tutorial.ipynb), [.py](tutorial8/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial8/tutorial.html)]|
-POD-RBF for modelling Lid Cavity| [[.ipynb](tutorial14/tutorial.ipynb), [.py](tutorial14/tutorial.py), [.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial14/tutorial.html)]|
+Introductory Tutorial: Supervised Learning with PINA |[[.ipynb](tutorial20/tutorial.ipynb),[.py](tutorial20/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial20/tutorial.html)]|
+Chemical Properties Prediction with Graph Neural Networks |[[.ipynb](tutorial15/tutorial.ipynb),[.py](tutorial15/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial15/tutorial.html)]|
+Unstructured Convolutional Autoencoders with Continuous Convolution |[[.ipynb](tutorial4/tutorial.ipynb),[.py](tutorial4/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial4/tutorial.html)]|
+Reduced Order Modeling with POD-RBF and POD-NN Approaches for Fluid Dynamics| [[.ipynb](tutorial8/tutorial.ipynb),[.py](tutorial8/tutorial.py),[.html](http://mathlab.github.io/PINA/_rst/tutorials/tutorial8/tutorial.html)]|
+