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Accelerated Time-domain Analysis for Gravitational Wave Astronomy

Vaishak Prasad

Abstract

Most current compact-binary searches and parameter-estimation pipelines evaluate the Gaussian-noise likelihood approximately using frequency-domain inner products with great success in analyzing gravitational-wave signals. This is historically motivated by (i) the approximate stationarity of detector noise on sufficiently long timescales, allowing a circulant approximation in the domain that diagonalizes the noise covariance in the Fourier basis, and (ii) the efficiency of matched filtering via fast Fourier transforms. However, the advantage of frequency-domain analysis comes with its own limitations. In this article, we develop a self-contained, end-to-end, \emph{fully time-domain} formulation of gravitational-wave inference and present an implementation that makes the likelihood evaluation practical at scale by exploiting structured linear algebra, software, and hardware acceleration. We validate the method using injections and demonstrate speedups for likelihood evaluation and on modern GPUs. We present \emph{tdanalysis}, an accelerated implementation that handles gaps, sharp boundaries, and multiple disjoint segments, and supports GPUs. We demonstrate some of its applications in gravitational wave astronomy.

Accelerated Time-domain Analysis for Gravitational Wave Astronomy

Abstract

Most current compact-binary searches and parameter-estimation pipelines evaluate the Gaussian-noise likelihood approximately using frequency-domain inner products with great success in analyzing gravitational-wave signals. This is historically motivated by (i) the approximate stationarity of detector noise on sufficiently long timescales, allowing a circulant approximation in the domain that diagonalizes the noise covariance in the Fourier basis, and (ii) the efficiency of matched filtering via fast Fourier transforms. However, the advantage of frequency-domain analysis comes with its own limitations. In this article, we develop a self-contained, end-to-end, \emph{fully time-domain} formulation of gravitational-wave inference and present an implementation that makes the likelihood evaluation practical at scale by exploiting structured linear algebra, software, and hardware acceleration. We validate the method using injections and demonstrate speedups for likelihood evaluation and on modern GPUs. We present \emph{tdanalysis}, an accelerated implementation that handles gaps, sharp boundaries, and multiple disjoint segments, and supports GPUs. We demonstrate some of its applications in gravitational wave astronomy.
Paper Structure (26 sections, 13 equations, 8 figures)

This paper contains 26 sections, 13 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Data model and time-domain likelihood
  3. Whitened representation
  4. Implementation details
  5. Cost analysis and Likelihood acceleration techniques for the time domain likelihood
  6. Algorithmic acceleration and Complexity analysis
  7. Data projection and conditioning
  8. Factorization of the Covariance matrix
  9. Gohlberg - Semencul theorem and Convolution / FFT-based method:
  10. Reduced-basis compressions:
  11. Hardware acceleration
  12. Memory bandwidth
  13. CPU acceleration
  14. GPU acceleration
  15. Software acceleration
  16. ...and 11 more sections

Figures (8)

  • Figure 1: Average amount of CPU FLOPs for 32-bit arithmetic and the memory bandwidth since 1990
  • Figure 2: The tdanalysis infrastructure for time domain analysis. This class diagram shows the basic skeleton of inheritance and composition for the major likelihood classes involved.
  • Figure 3: The estimated autocorrelation and PSD around the GW230814 event.
  • Figure 4: Caption
  • Figure 5: Benchmark results for direct Cholesky decomposed whitening operator method, and the GSCE method. The left plot shows the combined number of likelihood calls per second of the sampler across the multiprocessing pool on the left axis, and the single likelihood evaluation time on the right axis. The plot in the centre shows the performance of the GSCE method. The right panel shows the ratio of likelihood evaluation time on the device specified on the x-axis to that of a frequency domain likelihood evaluation on a CPU
  • ...and 3 more figures