Multi-variable integration with a neural network

In this article we present a method for automatic integration of parametric integrals over the unit hypercube using neural network. The fits network to primitive integrand loss function designed minimize difference between multiple derivatives and be integrated. We apply two example resulting from sector decomposition one-loop two-loop scalar integrals. Our can achieve per-mil percent accuracy these range invariant values. Once is fitted, evaluation integral 40 125 times faster than usual numerical our examples, expect speed gain increase with complexity integrand.