Technical Report: Toward a Scalable Algorithm to Compute High-Dimensional Integrals of Arbitrary Functions

Abstract

Neutron experiments at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory (ORNL) frequently generate large amounts of data (on the order of 106-1012 data points). Hence, traditional data analysis tools run on a single CPU take too long to be practical and scientists are unable to efficiently analyze all data generated by experiments. Our goal is to develop a scalable algorithm to efficiently compute high-dimensional integrals of arbitrary functions. This algorithm can then be used to integrate the four-dimensional integrals that arise as part of modeling intensity from the experiments at the SNS. Here, three different one-dimensional numerical integration solvers from the GNU Scientific Library were modified and implemented to solve four-dimensional integrals. The results of these solvers on a final integrand provided by scientists at the SNS can be compared to the results of other methods, such as quasi-Monte Carlo methods, computing the same integral. A parallelized version of the most efficient method can allow scientists the opportunity to more effectively analyze all experimental data.