Fast high-dimensional integration using tensor networks

TL;DR

This paper introduces tensor network methods for high-dimensional integration, demonstrating they outperform Monte Carlo and achieve exponential convergence even for non-analytic functions.

Contribution

It presents regression-free tensor network representations for integration, showing improved efficiency and convergence over traditional Monte Carlo methods.

Findings

Tensor network methods outperform Monte Carlo in test problems.

Exponential convergence achieved for non-analytic integrand.

Regression-free tensor network representations are effective for high-dimensional integration.

Abstract

The design and application of regression-free tensor network representations for integration is presented. Tensor network methods are demonstrated to outperform Monte Carlo for test problems, and exponential convergence is shown to be achievable for a non-analytic integrand.