Multi-variable integration with a neural network

Maître, D.; Santos-Mateos, R.

Abstract

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. Once the neural network is fitted, the evaluation of the integral is between 40 and 125 times faster than the usual numerical integration method for our examples, and we expect the speed gain to increase with the complexity of the integrand.

• Journal Article Type: Article
• Acceptance Date: Mar 14, 2023
• Online Publication Date: Mar 28, 2023
• Publication Date: 2023
• Deposit Date: Jun 19, 2023
• Publicly Available Date: Jun 19, 2023
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2023
• Issue: 3
• DOI: https://doi.org/10.1007/jhep03%282023%29221
• Public URL: https://durham-repository.worktribe.com/output/1172279