A dual neural network method for the solving of Multiple definite integral

• 1、College of Science,Inner Mongolia University of Technology, Hohhot 010051

Abstract：For the inefficient , less accurate and hard-to-solve problem existing in multiple definite integrals , in this study , a calculation method based on dual neural networks for the solving of multiple definite integrals is presented. Firstly, a dual neural network to construct the original function of the integral problem is presented, which theoretically proves that the method has the ability to approximate the original function of any integrand with arbitrary precision. On this basis, a neural network method for solving multiple deterministic integrals with arbitrary upper and lower bounds is obtained by applying the dual neural network method of constructing the original function repeatedly. The simulation results show that this method is an efficient and high - precision numerical method for solving multiple integral problems. The advantages of the method are: (1) The problem of multiple integration whose integral limits is functions. (2) Only a limited set of sample points of the integrand is known, without knowing the specific analytic expression of the integrand. (3) The implementation of the method is not limited by the number of integrals.

Keywords： Dual neural network Multiple definite integral Arbitrary integral domain