Neural Network Based on Orthogonal Legendre Polynomials for Solving Stochastic It?-Volterra Integral Equation
In order to solve the approximate solution of the multi-dimensional stochastic Itô-Volterra integral equation,the Legendre polynomial function approximation and the operation matrix with ligand method are used to convert the stochastic Itô-Volterra integral equation into algebraic equations.The loss function is constructed based on the operator matrix,and the neural network is constructed by using the configuration points as the network input and the coefficients of the Legendre polynomials as the weights.The approximate solutions are obtained by using the gradient descent method to learn the weights,and the corresponding convergence is analyzed theoretically.Finally,numerical examples are given to verify the accuracy of the proposed method.
Legendre polynomialoperation matrixneural networkstochastic integral equation
NETL
NSTL
万方数据
