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Update README.md (#17)

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* fix poisson equation on readme
* delete poisson_problem.png
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Nicola Demo
2022-06-23 11:53:50 +02:00
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@@ -45,10 +45,8 @@ PINN is a novel approach that involves neural networks to solve supervised learn
#### Problem definition #### 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. 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: Consider:
<p align="center"> $$\begin{cases}\nabla u = \sin(\pi x)\sin(\pi y)\quad& \text{in}\\,D,\\\\u = 0& \text{on}\\,\partial D,\end{cases}$$
<img alt="Poisson approximation" src="readme/poisson_problem.png" width="50%" /> 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:
</p>
where *D* is a square domain, *Gamma*s are the boundaries 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 ```python
class Poisson(SpatialProblem): class Poisson(SpatialProblem):

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