Random template banks and relaxed lattice coverings

TL;DR

This paper explores probabilistic methods for constructing template banks in gravitational wave searches, demonstrating that random and relaxed lattice coverings can significantly reduce the number of templates needed, especially in higher dimensions.

Contribution

It introduces and analyzes random and relaxed lattice template banks that cover parameter spaces with less templates by allowing incomplete coverage, improving efficiency at high dimensions.

Findings

Random template banks are surprisingly efficient and simple to implement.

Relaxed An* lattice covers are most efficient at low dimensions.

Random template banks outperform traditional lattice coverings at high dimensions.

Abstract

Template-based searches for gravitational waves are often limited by the computational cost associated with searching large parameter spaces. The study of efficient template banks, in the sense of using the smallest number of templates, is therefore of great practical interest. The "traditional" approach to template-bank construction requires every point in parameter space to be covered by at least one template, which rapidly becomes inefficient at higher dimensions. Here we study an alternative approach, where any point in parameter space is covered only with a given probability < 1. We find that by giving up complete coverage in this way, large reductions in the number of templates are possible, especially at higher dimensions. The prime examples studied here are "random template banks", in which templates are placed randomly with uniform probability over the parameter space. In addition to its obvious simplicity, this method turns out to be surprisingly efficient. We analyze the statistical properties of such random template banks, and compare their efficiency to traditional lattice coverings. We further study "relaxed" lattice coverings (using Zn and An* lattices), which similarly cover any signal location only with probability < 1. The relaxed An* lattice is found to yield the most efficient template banks at low dimensions (n < 10), while random template banks increasingly outperform any other method at higher dimensions.