Статья: Sampling of integrand for integration using shallow neural network

In this paper, we study the effect of using the Metropolis–Hastings algorithm for sampling the integrand on the accuracy of calculating the value of the integral with the use of shallow neural network. In addition, a hybrid method for sampling the integrand is proposed, in which part of the training sample is generated by applying the Metropolis–Hastings algorithm, and the other part includes points of a uniform grid. Numerical experiments show that when integrating in high-dimensional domains, sampling of integrands both by the Metropolis–Hastings algorithm and by a hybrid method is more efficient with respect to the use of a uniform grid.