Auto-encoder model for faster generation of effective one-body gravitational waveform approximations

TL;DR

This work tackles the computational bottleneck in gravitational-wave parameter estimation by introducing a conditional variational auto-encoder that rapidly generates aligned-spin SEOBNRv4 IMR waveforms across a four-parameter space. By decomposing waveforms into amplitude and instantaneous frequency components and employing a 2C2E1D CVAE with conditioning on source parameters, the method achieves median polarization mismatches around 10^-2 and generates hundreds of waveforms in roughly 0.1 seconds on GPUs, orders of magnitude faster than traditional methods. The results reveal strong performance within a restricted effective spin range, reveal the latent-space uncertainty inherent to VAEs, and point to future work including expanded parameter spaces, split-inspiral/merger models, and production-ready pipelines for online parameter estimation. Overall, this study lays groundwork for on-the-fly, ML-driven gravitational waveform approximations that can significantly accelerate rapid multi-messenger follow-ups and Bayesian inference in next-generation observatories.

Abstract

Upgrades to current gravitational wave detectors for the next observation run and upcoming third-generation observatories, like the Einstein telescope, are expected to have enormous improvements in detection sensitivities and compact object merger event rates. Estimation of source parameters for a wider parameter space that these detectable signals will lie in, will be a computational challenge. Thus, it is imperative to have methods to speed-up the likelihood calculations with theoretical waveform predictions, which can ultimately make the parameter estimation faster and aid in rapid multi-messenger follow-ups. Towards this end, we present a conditional variational auto-encoder model, based on the best performing architecture of Liao+2021, for faster generation of aligned-spin SEOBNRv4 inspiral-merger-ringdown waveforms. Our parameter space consists of four parameters, [$m_1$, $m_2$, $χ_1(z)$, $χ_2(z)$]. The masses are uniformly sampled in $[5,75]\,M_{\odot}$ with a mass ratio limit at $10\,M_{\odot}$, while the spins are uniform in $[-0.99,0.99]$. We train the model using $\sim10^5$ input waveforms data with a 70\%/10\% train/validation split, while 20\% data are reserved for testing. The median mismatch for the generated waveforms in the test dataset is $\sim10^{-2}$, with better performance in a restricted parameter space of $χ_{\rm eff}\in[-0.80,0.80]$. Our model is able to generate 100 waveforms in 0.1 second at an average speed of about 4.46 ms per waveform. This is 2-3 orders of magnitude faster than the native SEOBNRv4 implementation in lalsimulation. The latent sampling uncertainty of our model can be quantified with a mean mismatch deviation of $2\times10^{-1}$ for 1000 generations of the same waveform. Our work aims to be the first step towards developing a production-ready machine learning framework for the faster generation of gravitational waveform approximations.

Figures (10)

• Figure 1: Representative plot of a gravitational waveform time series used for training and then generating targets later. A gravitational polarization waveform can be converted to an amplitude and frequency series.
• Figure 2: The duration of a waveform as a function of the binary component masses and the lower frequency cut-off, showing iso-surfaces of equal durations at 1s, 5s, 10s, 20s and 30s.
• Figure 3: Architecture of the 2 conditionals, 2 encoder, 1 decoder (2C2E1D) auto-encoder model used in our analysis. The left side is the architecture used for training, while the right side is at the evaluation stage. Notice that the encoders are removed during evaluation and only the conditional parameter labels are used to generate outputs. See discussion for more details.
• Figure 4: Various loss function component values plotted against cumulative steps during the training and validation stages.
• Figure 5: Overplot of the reconstructed waveform approximation with the original polarization time series for a randomly selected set of input parameters from the test dataset.