A Neural Network Architecture for Obtaining Numerical Solutions of Integral Equation

This work proposes a neural network based approach using Gated Recurrent Unit neural network to solve integral equations. The proposed method employs Monte Carlo method to discretize the integral equations into a set of linear algebraic equations followed by a neural network based method to obtain numerical solutions. We demonstrate the versatility of our proposed systems using a numerical example of the second kind of Fredholm Integral equations. Adaptive moment estimation (ADAM) optimization has been used in the neural network to find the convergence. Clear illustrations with the use of loss function graphs, solution curve pertaining to actual and predicted function values are provided to help understand the behaviour of the solutions.