Nonlinear Inverse Problems for Von Karman Equations: A Neural Network Approximation
Natalia I. Obodan
Oles Honchar Dnipro National University, Dnipro, Ukraine.
Oleksii S. Mahas *
Oles Honchar Dnipro National University, Dnipro, Ukraine.
Vasilii A. Gromov
Oles Honchar Dnipro National University, Dnipro, Ukraine.
*Author to whom correspondence should be addressed.
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.
Keywords: The coefficient inverse problem, nonlinear boundary problem, von Karman equations, the inverse operator, the Fréchet differentiability, neuro-evolution augmented topologies.