Numerical solution of inverse problems by weak adversarial networks

Numerical solution of inverse Sturm–Liouville problems

A new algorithm is proposed for solving the inverse Sturm–Liouville problem of reconstructing a symmetric potential from eigenvalues. It uses Numerov’s method instead of the second order method of the related algorithm of Fabiano, Knobel and Lowe. An extension by Andrew and Paine of the asymptotic correction technique of Paine, de Hoog and Anderssen is the key to the success of the new algorith...

Multi-Level Approach to Numerical Solution of Inverse Problems

Mathematical modeling of an engineering system often leads to such formulations for which one can not obtain a closed form solution/analysis, and thus numerical methods are to be used. In the process, we need to transform the system from an infinite dimensional space to a finite dimensional one(discretization). The result is usually a system of linear equations[5] for which the linear least squ...

Numerical Solution of Inverse Heat Transfer Problems by Parameters Estimation of Ordinary Differential Equations

In this paper, algorithms for solving of two inverse onedimensional heat transfer problems are considered. They are: the coe cient inverse problem and the determination of phase interface location in a melting problem. These inverse problems are reduced to parameters estimation of ordinary di erential equations (ODE) using a nite element method. The algorithm based on the sensitivity analysis i...

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 degr...

Numerical Solution of Limited-data Inverse Problems Arising from X-ray Tomography and Acoustic Inverse Scattering