Tensorflow-based Neural Network For Fredholm Integral Equation

Neural networks have been successfully applied in image recognition,speech recog-nition,and sentiment analysis,and have wide application prospects in various fields.Based on Tensorflow,this paper proposes a numerical method for solving Fredholm in-tegral equations using residual networks.Firstly,a set of random points in the domain are generated as the training data.And the values at these points are predicted by for-ward residual neural network.The loss function is defined by substituting the predicted values into the Fredholm integral equation.Then solving Fredholm integral equation is transformed into a least squares problem,and neural network is used to solve the least squares problem.This method has a simple form,does not significantly increase the cost for high-dimensional problems.Numerical experimental results show that the residuals neural networks not only does not suffer from network degradation,but also has the ad-vantages of good stability and strong generalization ability.The new method can solve the Fredholm integral equations efficiently and accurately.