标题： 基于自回归神经网络流的引力波参数估计 显示英文标题

标题： Gravitational-wave parameter estimation with autoregressive neural network flows

摘要： 我们介绍了利用自回归归一化流（autoregressive normalizing flows）进行基于深度神经网络的引力波数据二元黑洞系统参数的快速似然无偏推断的方法。 归一化流是一种可逆映射，可以用于从简单概率分布到更复杂概率分布的变换：如果简单分布能够快速采样且其密度函数可以被评估，则复杂分布也可以如此。 我们的首个引力波应用使用了条件于探测器应变数据的自回归流，将多元标准正态分布映射到系统参数的后验分布上。 我们在由五参数 $(m_1, m_2, \phi_0, t_c, d_L)$ 先验下的 IMRPhenomPv2 波形和具有固定功率谱密度的平稳高斯噪声实现的人工应变数据上训练该模型，其性能与当前最佳的深度学习引力波参数估计方法相当。 然后，我们将自回归流融入变分自编码器框架中，构建了一个更强大的潜在变量模型。此模型的性能与马尔科夫链蒙特卡洛（Markov chain Monte Carlo）相当，并且尤其成功地建模了多峰 $\phi_0$ 后验分布。 最后，我们在扩展的参数空间上训练自回归潜在变量模型，包括平行自旋 $(\chi_{1z}, \chi_{2z})$ 和双星倾斜角 $\theta_{JN}$，并证明所有参数及其退化关系均能良好恢复。在所有情况下，采样速度极快，在不到两秒的时间内即可抽取 $10^4$ 后验样本。 显示英文摘要

摘要： We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one: if the simple distribution can be rapidly sampled and its density evaluated, then so can the complex distribution. Our first application to gravitational waves uses an autoregressive flow, conditioned on detector strain data, to map a multivariate standard normal distribution into the posterior distribution over system parameters. We train the model on artificial strain data consisting of IMRPhenomPv2 waveforms drawn from a five-parameter $(m_1, m_2, \phi_0, t_c, d_L)$ prior and stationary Gaussian noise realizations with a fixed power spectral density. This gives performance comparable to current best deep-learning approaches to gravitational-wave parameter estimation. We then build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework. This model has performance comparable to Markov chain Monte Carlo and, in particular, successfully models the multimodal $\phi_0$ posterior. Finally, we train the autoregressive latent variable model on an expanded parameter space, including also aligned spins $(\chi_{1z}, \chi_{2z})$ and binary inclination $\theta_{JN}$, and show that all parameters and degeneracies are well-recovered. In all cases, sampling is extremely fast, requiring less than two seconds to draw $10^4$ posterior samples.