Neural Network Based Solution to Inverse Problems

The weILposedr7ess of the problems is not always guaranteed in inverse problems, unlike the forward problems. Dnts, a number of methods for giving wellposedrjess hm?e been studied in mathematical fields. In the ,field qf neural! networks, the network inversion method. for solving inverse problems was proposed; it is useflll but does not dissolute the ill-posedness of inverse problems. To overcome the difficulty, we propose the answer-in-weights scheme to prollide the network with a priori given knowledge. In this paper, we compared the perfor&ance of answer-in-weights network with the one qf inversion network in solving the ill-posed inverse problem arising in the Fredholm integral equation of the first kind. Furthermore, we compared the express&n of the a priori knowledge inherent to the problem, by using two kinds of models.