We introduce a numerical framework for reconstructing the potential \(q\) in two dimensional
semilinear elliptic PDEs with power-type nonlinearities. We consider
\begin{equation*}\label{eq:nonlinear}
-\Delta u + q(x)\,u^{p} = 0 \quad \text{in }\Omega,\qquad
u\big|_{\partial\Omega} = f,
\end{equation*}
with \(p\in\mathbb{N}_{\ge 2}\), on a bounded domain \(\Omega\subset\mathbb{R}^2\) and Dirichlet data \(f\).
Given boundary measurements associated with the equation, our goal is to recover \(q\).
We study this numerically using the higher order linearization method for semilinear Calder\`on type problems: we differentiate the nonlinear Dirichlet to Neumann (DN) map to obtain
auxiliary linearized equations, from which we compute Fourier data of the unknown potential and
then invert it using Tikhonov or TV regularization to reconstruct \(q\). This enables reconstruction even in settings where the corresponding
linear inverse problem is difficult to resolve. This is a joint work with Teemu Tyni and Matti Lassas.