  We establish Lipschitz stability properties for a class of inverse problems.
In that class, the associated direct problem is formulated by an integral
operator Am depending non-linearly on a parameter m and operating on a function
u. In the inversion step both u and m are unknown but we are only interested in
recovering m. We discuss examples of such inverse problems for the elasticity
equation with applications to seismology and for the inverse scattering problem
in electromagnetic theory. Assuming a few injectivity and regularity properties
for Am, we prove that the inverse problem with a finite number of data points
is solvable and that the solution is Lipschitz stable in the data. We show a
reconstruction example illustrating the use of neural networks.
