New Tutorials and Tutorial manifesto

[dario-coscia]

Is your feature request related to a problem? Please describe. It would be nice to restructure the Tutorials to be more modular and introduce from zero the users to PINA. Here I try to provide a possible suggestion

Getting started with PINA

• Getting started with PINA in 4 steps: Problem, Model, Solver and Trainer (new)
• Data structures in PINA (new) from Graph to LabelTensor (new)
• Building custom geometries with PINA Domain class (update name)
• Introduction to PINA Equation class (I think it should be updated to have more stuff in it)
• Build a Problem in PINA step by step (new)
• What’s a Solver and how to build a custom one in PINA (new)
• Introduction to PINA Trainer (just rename the one on pina and lightning)
• How to boost PINA performance? Speed and memory efficient training tips (new)

Physics Informed Neural Networks

• Introduction to PINA for Physics Informed Networks
• …. (Existing tutorials)

Neural Operator Learning

• Introduction to PINA to Neural Operator Learning (new)
• …. (Existing tutorials)

Supervised Learning

• Introduction to PINA to Supervised Learning (new)
• A tutorial on graph (new)
• …. (Existing tutorials)

Generative Modeling (new)

• Introduction to PINA Generative modeling (new)

Developers tutorials (new)

• Debugging and Profiling PINA (new)

Also, I think we should add a Tutorial manifesto saying what it can be included as tutorial and what it cannot. This is to avoid to have many repeated tutorials (e.g. at the moment we have 2 tutorials on ROM which do the exact same thing...)