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Nicola Demo
2022-06-23 11:57:08 +02:00
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@@ -45,7 +45,7 @@ PINN is a novel approach that involves neural networks to solve supervised learn
#### Problem definition
First step is formalization of the problem in the PINA framework. We take as example here a simple Poisson problem, but PINA is already able to deal with **multi-dimensional**, **parametric**, **time-dependent** problems.
Consider:
$$\begin{cases}\nabla u = \sin(\pi x)\sin(\pi y)\quad& \text{in}\\,D,\\\\u = 0& \text{on}\\,\partial D,\end{cases}$$
$$\begin{cases}\Delta u = \sin(\pi x)\sin(\pi y)\quad& \text{in}\\,D,\\\\u = 0& \text{on}\\,\partial D,\end{cases}$$
where $D = [0, 1]^2$ is a square domain and $u$ the unknown field. The translation in PINA code becomes a new class containing all the information about the domain, about the `conditions` and nothing more:
```python