update doc

Author: dario-coscia

docs/source/_installation.rst

@@ -1,7 +1,7 @@
 Installation
 ============
 
-**PINA** requires requires `numpy`, `matplotlib`, `torch`, `lightning`, `sphinx` (for the documentation) and `pytest` (for local test). The code is tested for Python 3, while compatibility of Python 2 is not guaranteed anymore. It can be installed using `pip` or directly from the source code.
+**PINA** requires requires `torch`, `lightning`, `torch_geometric` and `matplotlib`. 
 
 Installing via PIP
 __________________
@@ -32,3 +32,21 @@ To install the package just type:
 .. code-block:: bash
 
     $ pip install -e .
+
+
+Install with extra packages
+____________________________
+
+To install extra dependencies required to run tests or tutorials directories, please use the following command:
+
+.. code-block:: bash
+
+    $ pip install "pina-mathlab[extras]" 
+
+
+Available extras include:
+
+* `dev` for development purpuses, use this if you want to Contribute.
+* `test` for running test locally.
+* `doc` for building documentation locally.
+* `tutorial` for running tutorials

docs/source/_rst/_code.rst

@@ -3,7 +3,7 @@ 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
+.. figure:: ../index_files/PINA_API.png
     :alt: PINA application program interface
     :align: center
     :width: 400

docs/source/index.rst

@@ -1,6 +1,6 @@
 :html_theme.sidebar_secondary.remove:
 
-Welcome to PINA’s documentation!
+Welcome to PINA's documentation!
 =======================================
 
 .. grid:: 6
@@ -41,35 +41,36 @@ Welcome to PINA’s documentation!
   .. grid-item::
     :columns: 12 12 8 8
 
-    Physics Informed Neural network for Advanced modeling (**PINA**) is
-    an open-source Python library providing an intuitive interface for
-    solving differential equations using PINNs, NOs or both together.
+    **PINA** is an open-source Python library designed to simplify and accelerate 
+    the development of Scientific Machine Learning (SciML) solutions.
+    Built on top of `PyTorch <https://pytorch.org/>`_, `PyTorch Lightning <https://lightning.ai/docs/pytorch/stable/>`_, 
+    and `PyTorch Geometric <https://pytorch-geometric.readthedocs.io/en/latest/>`_, 
+    PINA provides an intuitive framework for defining, experimenting with, 
+    and solving complex problems using Neural Networks, 
+    Physics-Informed Neural Networks (PINNs), Neural Operators, and more.
 
-    Based on `PyTorch <https://pytorch.org/>`_, `PyTorchLightning <https://lightning.ai/docs/pytorch/stable/>`_, and `PyG <https://pytorch-geometric.readthedocs.io/en/latest/>`_, **PINA** offers a simple and intuitive way to formalize a specific (differential) problem
-    and solve it using neural networks . The approximated solution of a differential equation
-    can be implemented using PINA in a few lines of code thanks to the intuitive and user-friendly  interface.        
+    - **Modular Architecture**: Designed with modularity in mind and relying on powerful yet composable abstractions, PINA allows users to easily plug, replace, or extend components, making experimentation and customization straightforward.
 
- 
+    - **Scalable Performance**: With native support for multi-device training, PINA handles large datasets efficiently, offering performance close to hand-crafted implementations with minimal overhead.
+
+    - **Highly Flexible**: Whether you're looking for full automation or granular control, PINA adapts to your workflow. High-level abstractions simplify model definition, while expert users can dive deep to fine-tune every aspect of the training and inference process.
 
     For further information or questions about **PINA** contact us by email. 
 
-
-   
-
   .. grid-item-card:: Contents
     :class-title: sd-fs-5
     :class-body: sd-pl-4
 
     .. toctree::
       :maxdepth: 1
 
-      API <_rst/_code>
-      Tutorial <_tutorial>
       Installing <_installation>
-      Team & Foundings <_team.rst>
+      API <_rst/_code>
+      Tutorials <_tutorial>
+      Cite PINA <_cite.rst>
       Contributing <_contributing>
+      Team & Foundings <_team.rst>
       License <_LICENSE.rst>
-      Cite PINA <_cite.rst>