A numerical approach for the fractional Laplacian via deep neural
  networks
Nicolás Valenzuela
We consider the fractional elliptic problem with Dirichlet boundary
conditions on a bounded and convex domain $D$ of $\mathbb{R}^d$, with $d \geq
2$. In this paper, we perform a stochastic gradient descent algorithm that
approximates the solution of the fractional problem via Deep Neural Networks.
Additionally, we provide four numerical examples to test the efficiency of the
algorithm, and each example will be studied for many values of $\alpha \in
(1,2)$ and $d \geq 2$.