Real-time gravitational-wave inference for binary neutron stars using machine learning

TL;DR

The paper tackles real-time inference for binary neutron star gravitational-wave signals, whose long durations challenge traditional Bayesian methods. It introduces Dingo-BNS, a simulation-based inference framework that uses prior conditioning, heterodyning, frequency multibanding, and frequency masking to compress data and enable full parameter estimation in about one second, including pre-merger analysis. The EOS likelihood is computed by integrating the posterior along EOS-imposed hyperplanes, using fast SBI routes and importance sampling to guarantee asymptotic exactness. This approach yields near real-time, high-fidelity localization and source-parameter information, improves sky localization by ~30% over fast Bayestar methods, and scales to hour-long signals for next-generation detectors, with significant implications for multi-messenger astronomy and neutron-star physics.

Abstract

Mergers of binary neutron stars (BNSs) emit signals in both the gravitational-wave (GW) and electromagnetic (EM) spectra. Famously, the 2017 multi-messenger observation of GW170817 led to scientific discoveries across cosmology, nuclear physics, and gravity. Central to these results were the sky localization and distance obtained from GW data, which, in the case of GW170817, helped to identify the associated EM transient, AT 2017gfo, 11 hours after the GW signal. Fast analysis of GW data is critical for directing time-sensitive EM observations; however, due to challenges arising from the length and complexity of signals, it is often necessary to make approximations that sacrifice accuracy. Here, we present a machine learning framework that performs complete BNS inference in just one second without making any such approximations. Our approach enhances multi-messenger observations by providing (i) accurate localization even before the merger; (ii) improved localization precision by $\sim30\%$ compared to approximate low-latency methods; and (iii) detailed information on luminosity distance, inclination, and masses, which can be used to prioritize expensive telescope time. Additionally, the flexibility and reduced cost of our method open new opportunities for equation-of-state studies. Finally, we demonstrate that our method scales to extremely long signals, up to an hour in length, thus serving as a blueprint for data analysis for next-generation ground- and space-based detectors.

Figures (10)

• Figure 1: Real-time GW inference for BNS is enabled by several innovations. (a) Dingo-BNS estimates all BNS parameters in just one second (orange), reproducing LVK results Abbott:2018wiz (black) three orders of magnitude faster than existing methods Morisaki:2023kuqWong:2023lgb. Dingo-BNS can also analyze partial data before the merger occurs (teal). Fast analysis results are crucial for directing electromagnetic searches for prompt or even precursor signals. Note that GW170817 overlapped with a loud glitch, which could explain why the true sky position lies in the tail of the pre-merger distribution. (b) For a given event, the chirp mass posterior (black) is tightly constrained compared to the prior (blue), so a restricted chirp mass prior (orange) is sufficient, and moreover simplifies analysis. With our prior-conditioning technique, we train a single neural network that can be instantly tuned to an event-specific prior lying anywhere within the full volume. (c) We compress data by a factor of $\sim 100$ by first factoring out ("heterodyning") the predominant phase evolution of the signal (blue), based on a chirp mass estimate ${\widetilde{\mathcal{M}}}$ associated to the event-specific prior. The resulting simplified signal (orange) is down-sampled in resolution, reducing data dimensionality (coarser resolution at high frequencies; bands indicated by dotted red lines). (d) To enable pre-merger inference, we mask out the strain frequency series according to the cut-off time. (e) All of these components are integrated into a single neural network that can be trained end-to-end and produce $10^5$ weighted samples per second, with typical sampling efficiencies of 50%.
• Figure 2: Pre-merger inference with Dingo-BNS. (a) Evolution of pre-merger estimates for GW170817 (black) and GW170817-like simulations injected into different noise levels (colors). We display the 90% credible sky area, the standard deviation of the chirp mass, the accumulated signal-to-noise and the log Bayes factor comparing the signal and noise models. All of these quantities are inferred with a latency of $\sim1$ second. Dotted lines represent 10th/90th percentiles. (b) Sky localization area at 90% credible level for various premerger times, comparing against Bayestar. The boxplots display the median (red line), quartiles (colored box) and 10th/90th percentiles (whiskers). Dingo-BNS localization is consistently more precise. (c) Premerger sky localization for a GW170817-like event injected into Cosmic Explorer noise, using a minimum frequency of 6 Hz. The black marker indicates the injection coordinates, and gray outline the 90% credible area.
• Figure 3: Prior conditioning enables event-specific compression. We train an SBI model simultaneously across a range of priors, each parametrized by a reference chirp mass ${\widetilde{\mathcal{M}}}$. For each (narrow) prior $p_{\widetilde{\mathcal{M}}}(\mathcal{M})$, we apply heterodyning and multibanding compression. This compression simplifies the data distribution that the model must learn and reduces its dimensionality. For simplicity in this presentation, we omit parameters other than the chirp mass.
• Figure 4: (a) Log likelihoods generated from a scan over different values of ${\widetilde{\mathcal{M}}}$ with a Dingo-BNS network. The final ${\widetilde{\mathcal{M}}}$ is chosen as the maximum likelihood $\mathcal{M}$ (red line; ${\widetilde{\mathcal{M}}}=1.1975~\text{M}_\odot$ for GW170817, ${\widetilde{\mathcal{M}}}=1.4868~\text{M}_\odot$ for GW190425). (b) Posterior marginal $p(\mathcal{M}|d)$. The prior (dashed lines) determined by the scan from (a) fully covers the marginal. (c) A combined scan over $\mathcal{M}$ and $t_\text{c}$ successfully identifies GW170817 (with $\hat{t}_\text{c}=1187008882.43$) and GW190425 (with $\hat{t}_\text{c}=1240215503.04$).
• Figure 5: Frequency multibanding. (a) The period of (heterodyned) GW signals decreases with increasing frequency. The native frequency resolution (blue) thus oversamples the signal at high frequencies. Frequency multibanding (band boundaries indicated by dotted red lines) adapts to the signal variation, decreasing the resolution at higher frequencies (orange). (b) The multibanded domain therefore requires fewer frequency bins, and the signal variation is more homogeneous across bins. (c) Multibanded frequency domain partitions for LVK ($f_\text{min} = 19.4~\text{Hz}$, compression factor $\sim 60$) and CE ($f_\text{min} = 5\,\text{Hz}$, compression factor $\sim 650$) experiments. We use a smaller chirp mass prior for the CE experiments (Tab. \ref{['tab:priors']}), which allows a slightly coarser resolution compared to LVK (corresponding to lower $\hat{f}_i$). The first two bands for CE are skipped entirely, which is a consequence of the reduced signal variation with heterodyning.