Group Determination of Parameters and Training with Noise Addition: Joint Application to Improve the Resilience of the Neural Network Solution of a Model Inverse Problem to Noise in Data

Abstract

Solution of inverse problems is usually sensitive to noise in the input data, as problems of this type are usually ill-posed or ill-conditioned. While neural networks have high noise resilience by themselves, this may be not enough in case of incorrect inverse problems. In their previous studies, the authors have demonstrated that the method of group determination of parameters, as well as noise addition during training of a neural network, can improve the resilience of the solution to noise in the input data. This study is devoted to the investigation of joint application of these methods. It has been performed on a model problem, for which the direct function is set explicitly as a polynomial.