Neural network application to solve Fredholm integral equations of the first kind

Summary form only given, as follows. Inverse problems appear often in many fields of science and engineering. The authors applied the neural network to obtain the numerical solution of Fredholm integral equations of the first kind, which defines a typical inverse problem. Under some a priori information on the relevant system, the network is able to learn an inverse mapping from an output function to an input function of the integral equations. It is shown by two examples that these inverse mappings are numerically stable and robust for the noisy input data.<>