Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy (1909.06296v4)

Abstract: Gravitational wave (GW) detection is now commonplace and as the sensitivity of the global network of GW detectors improves, we will observe $\mathcal{O}(100)$s of transient GW events per year. The current methods used to estimate their source parameters employ optimally sensitive but computationally costly Bayesian inference approaches where typical analyses have taken between 6 hours and 5 days. For binary neutron star and neutron star black hole systems prompt counterpart electromagnetic (EM) signatures are expected on timescales of 1 second -- 1 minute and the current fastest method for alerting EM follow-up observers, can provide estimates in $\mathcal{O}(1)$ minute, on a limited range of key source parameters. Here we show that a conditional variational autoencoder pre-trained on binary black hole signals can return Bayesian posterior probability estimates. The training procedure need only be performed once for a given prior parameter space and the resulting trained machine can then generate samples describing the posterior distribution $\sim 6$ orders of magnitude faster than existing techniques.

• The paper presents a CVAE approach that accelerates Bayesian parameter estimation by six orders of magnitude compared to conventional methods.
• It utilizes an encoder-decoder network trained on simulated BBH signals with specialized distributions for multi-detector data integration.
• Results on 250 simulated events demonstrate comparable accuracy to traditional inference, enabling real-time multi-messenger astronomy.

Bayesian Parameter Estimation Using Conditional Variational Autoencoders for Gravitational-Wave Astronomy

Introduction

In the field of gravitational-wave (GW) astronomy, the detection and analysis of gravitational waves from astrophysical events, such as binary black hole (BBH) mergers, have become a routine activity. The advent of advanced GW observatories like LIGO has facilitated the regular identification of such events, necessitating the development of efficient methodologies for estimating the parameters of GW sources. Traditional Bayesian inference methods, although optimal in sensitivity, are computationally demanding, often requiring between six hours and six days to perform a full analysis on a given event. Given the increasing incidence of detected events, there is a pressing need for faster approaches without compromising the accuracy of the parameter estimates.

Conditional Variational Autoencoder (CVAE) Approach

The paper introduces a novel approach utilizing conditional variational autoencoders (CVAE) for fast Bayesian parameter estimation in GW astronomy. The CVAE method is trained using a dataset of simulated BBH waveforms, which allows it to learn the relationship between simulated GW data and their corresponding source parameters. Once trained, the CVAE can generate samples from the posterior distribution much more quickly than traditional sampling methods, achieving speedups of approximately six orders of magnitude.

Technical Framework

The CVAE model consists of an encoder-decoder network structure. The encoder transforms input GW data into a latent space representation, which is then used by the decoder to predict the posterior distribution of the source parameters. During training, the model optimizes an evidence lower bound (ELBO), which includes the cross-entropy between the true and predicted distributions and a Kullback-Leibler (KL) divergence term that ensures the latent space representation is structured appropriately.

Key modifications tailored to GW signals include the use of von Mises-Fisher distributions for sky location parameters and truncated Gaussian distributions for parameters with predefined bounds. The model handles multi-detector data through a convolutional neural network architecture, integrating information from multiple GW detectors.

Results and Evaluation

The paper evaluated the CVAE model using a test set of 250 simulated GW events, comparing its performance against traditional Bayesian samplers using the Bilby library. Results demonstrated that the CVAE approach consistently produced parameter estimates with accuracy comparable to conventional methods, as evidenced by cumulative probability-probability (PP) plots and Jensen-Shannon (JS) divergence metrics. The model's speed advantage is particularly noteworthy, achieving equivalent inference quality in a fraction of a second—a critical capability for real-time multi-messenger astronomy.

Implications and Future Directions

The CVAE-based framework marks a significant step toward rapid and accurate parameter estimation in GW astronomy, addressing the computational challenges posed by the growing number of detections. This method is promising for extending analyses to other GW signals like binary neutron star and neutron star-black hole coalescences, particularly in contexts requiring rapid parameter estimation for follow-up electromagnetic observations. Future enhancements could include adapting the model for real detector noise and expanding its applicability to other types of gravitational events.

In conclusion, the integration of machine learning techniques such as CVAEs into GW parameter estimation workflows represents a valuable advancement, facilitating both increased efficiency and maintaining the high precision necessary for advancing our understanding of these cosmic phenomena.