Nonlinear Inverse Problems for Von Karman Equations: A Neural Network Approximation

Abstract

This paper considers the coefficient inverse problem for the nonlinear boundary problem of von Karman equations. The Fréchet differentiability of the inverse operator is proved and its neural network approximation is constructed with neuroevolution augmented topology model. The model used proves efficient to solve the coefficient inverse problem even for the parameters values close to those corresponding to singular solutions of the direct problem.