Multi-variable Integration with a Neural Network

Understand

In this article we present a method for automatic integration of parametric integrals over the unit hypercube using a neural network.

• The method fits a neural network to the primitive of the integrand using a loss function designed to minimize the difference between multiple derivatives of the network and the function to be integrated.
• We apply this method to two example integrals resulting from the sector decomposition of a one-loop and two-loop scalar integrals.
• Our method can achieve per-mil and percent accuracy for these integrals over a range of invariant values.