Efficient Stochastic Template Bank using Inner Product Inequalities

TL;DR

This paper presents a new stochastic method for constructing gravitational wave template banks that improves efficiency and flexibility, especially in high-dimensional parameter spaces, by using inner product inequalities and Gaussian Kernel Density Estimation.

Contribution

The authors introduce a novel stochastic placement technique utilizing inner product inequalities and Gaussian KDE to efficiently generate template banks for complex gravitational wave searches.

Findings

Method produces self-consistent banks that recover signals effectively.

Comparable performance and size to existing geometric and stochastic methods.

Significantly reduces computational load in high-dimensional parameter spaces.

Abstract

Gravitational wave searches are crucial for studying compact sources like neutron stars and black holes. Many sensitive modeled searches use matched filtering to compare gravitational strain data to a set of waveform models known as template banks. We introduce a new stochastic placement method for constructing template banks, offering efficiency and flexibility to handle arbitrary parameter spaces, including orbital eccentricity, tidal deformability, and other extrinsic parameters. This method can be computationally limited by the ability to compare proposal templates with the accepted templates in the bank. To alleviate this computational load, we introduce the use of inner product inequalities to reduce the number of required comparisons. We also introduce a novel application of Gaussian Kernel Density Estimation to enhance waveform coverage in sparser regions. Our approach has been employed to search for eccentric binary neutron stars, low-mass neutron stars, primordial black holes, supermassive black hole binaries. We demonstrate that our method produces self-consistent banks that recover the required minimum fraction of signals. For common parameter spaces, our method shows comparable computational performance and similar template bank sizes to geometric placement methods and stochastic methods, while easily extending to higher-dimensional problems. The time to run a search exceeds the time to generate the bank by a factor of $\mathcal{O}(10^5)$ for dedicated template banks, such as geometric, mass-only stochastic, and aligned spin cases, $\mathcal{O}(10^4)$ for eccentric and $\mathcal{O}(10^3)$ for the tidal deformable bank. With the advent of efficient template bank generation, the primary area for improvement is developing more efficient search methodologies.