Sampling of integrand for integration using shallow neural network

Inthispaper,westudytheeffectofusingtheMetropolis-Hastingsalgorithmforsamplingtheintegrand 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.