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fix doc/readme/joss (#146)

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* fix doc/readme/joss with API scheme

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Co-authored-by: Dario Coscia <dariocoscia@cli-10-110-11-236.WIFIeduroamSTUD.units.it>
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Dario Coscia
2023-07-04 11:52:10 +02:00
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@@ -62,12 +62,11 @@ Among all these frameworks, PINA wants to emerge for its easiness of usage, allo
Built over PyTorch --- in order to inherit the \verb+autograd+ module and all the other features already implemented --- PINA provides indeed documented API to explain usage and capabilities of the different classes. We have built several abstract interfaces not only for better structure of the source code but especially to give the final user an easy entry point to implement their own extensions, like new loss functions, new training procedures, and so on. This aspect, together with the capability to use all the PyTorch models, makes it possible to incorporate almost any existing architecture into the PINA framework.
We have decided to build it on top of PyTorch in order to exploit the \verb+autograd+ module, as well as all the other features implemented in this framework. The final outcome is then a library with incremental complexity, capable of being used by the new users to perform the first investigation using PINNs, but also as a core framework to actively develop new features to improve the discussed methodology.
The high-level structure of the package is illustrated in Figure \ref{API_visual}; 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.
The high-level structure of the package is depicted in our [API](https://github.com/mathLab/PINA/tree/master/readme/API_color.png); 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.
Besides the user-friendly interface, PINA also offers several examples and tutorials, aiming to guide new users toward an easy exploration of the software features. The online documentation is released at \url{https://mathlab.github.io/PINA/}, while the robustness of the package is continuously monitored by unit tests.
The API visualization in Figure \ref{API_visual} shows that a complete workflow in PINA is characterized by 3 main steps: the problem formulation, the model definition, i.e. the structure of the neural network used, and the training, eventually followed by the data visualization.
PINA workflow is characterized by 3 main steps: the problem formulation, the model definition, i.e. the structure of the neural network used, and the training, eventually followed by the data visualization.
![High-level structure of the library.\label{API_visual}](API_color.png){ width=70% }
## Problem definition in PINA
The first step is the formalization of the problem.