Artificial Neural Networks for the Solution of Inverse Problems

In this work we present a variational formulation for neural networks. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function which is an extremal for some functional. As we will see, a variational formulation for neural networks provides a direct method for the solution of general variational problems, in any dimension and up to any degree of accuracy. In order to validate this technique for the solution of inverse problems we train multilayer perceptron networks to solve an input estimation problem and a properties estimation problem.