diff --git a/README.md b/README.md index 5eb62aa..1cf69ac 100644 --- a/README.md +++ b/README.md @@ -55,13 +55,10 @@ 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: -$$ -\begin{cases} -\nabla u = \sin(\pi x) \sin(\pi y) & \quad\text{in}\, D,\\ -u = 0 &\quad\text{on}\, \Gamma_1 \cup\Gamma_2 \cup\Gamma_3 \cup\Gamma_4, \\ -\end{cases} -$$ -where $D= [0, 1]^2$ is a square domain, $\Gamma_1 \cup\Gamma_2 \cup\Gamma_3 \cup\Gamma_4$ 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: +

+ Poisson approximation +

+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 class Poisson(SpatialProblem): spatial_variables = ['x', 'y'] @@ -104,6 +101,9 @@ plotter = Plotter() plotter.plot(pinn) ``` After the training we can infer our model, save it or just plot the PINN approximation. +

+ Poisson approximation +

## Dependencies and installation diff --git a/readme/poisson_plot.png b/readme/poisson_plot.png new file mode 100644 index 0000000..cb3d6d8 Binary files /dev/null and b/readme/poisson_plot.png differ diff --git a/readme/poisson_problem.png b/readme/poisson_problem.png new file mode 100644 index 0000000..5931275 Binary files /dev/null and b/readme/poisson_problem.png differ