Topological derivative and neural network for inverse problems of coupled models

In the paper we consider a new method based on the neural network for finding the location of small holes in the domain, in which the coupled linear and nonlinear boundary value problems are defined. The linear and nonlinear components are connected by the transmission conditions on the interface boundary. We use an artificial neural network, which calculates the locations of hole in the linear component of the domain based of input data, coming from the exterior part of the domain and based on the topological derivative.