The LIGO and Virgo gravitational-wave observatories have detected many exciting events over the past 5 years. To infer the system parameters, iterative sampling algorithms such as MCMC are typically used with Bayes’ theorem to obtain posterior samples—by repeatedly generating waveforms and comparing to measured strain data. However, as the rate of detections grows with detector sensitivity, this poses a growing computational challenge. To confront this challenge, as well as that of fast multimessenger alerts, in this study we apply deep learning to learn non-iterative surrogate models for the Bayesian posterior. We train a neural-network conditional density estimator to model posterior probability distributions over the full 15-dimensional space of binary black hole system parameters, given detector strain data from multiple detectors. We use the method of normalizing flows—specifically, a neural spline flow—which allows for rapid sampling and density estimation. Training the network is likelihood-free, requiring samples from the data generative process, but no likelihood evaluations. Through training, the network learns a global set of posteriors: it can generate thousands of independent posterior samples per second for any strain data consistent with the training distribution. We demonstrate our method by performing inference on GW150914, and obtain results in close agreement with standard techniques.

LIGO 和 Virgo 引力波天文台在过去 5 年中探测到了许多激动人心的事件。为了推断系统参数，通常将 MCMC 等迭代采样算法与贝叶斯定理结合使用，通过重复生成波形并与测量的应变数据进行比较来获得后验样本。然而，随着检测率随着检测器灵敏度的增加而增加，这带来了越来越大的计算挑战。为了应对这一挑战以及快速多信使警报的挑战，在本研究中，我们应用深度学习来学习贝叶斯后验的非迭代代理模型。我们训练神经网络条件密度估计器，在给定来自多个探测器的探测器应变数据的情况下，对二元黑洞系统参数的整个 15 维空间上的后验概率分布进行建模。神经样条流——允许快速采样和密度估计。训练网络是无似然的，需要来自数据生成过程的样本，但不需要似然评估。通过训练，网络学习了一组全局后验概率：对于与训练分布一致的任何应变数据，它可以每秒生成数千个独立的后验样本。我们通过对 GW150914 进行推理来演示我们的方法，并获得与标准技术非常一致的结果。