The LIGO and Virgo gravitational-wave observatories have detected many exciting events over the past five years. As the rate of detections grows with detector sensitivity, this poses a growing computational challenge for data analysis. With this in mind, in this work we apply deep learning techniques to perform fast likelihood-free Bayesian inference for gravitational waves. 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 normalizing 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 prior and detector noise characteristics used for training. By training with the detector noise power spectral density estimated at the time of GW150914, and conditioning on the event strain data, we use the neural network to generate accurate posterior samples consistent with analyses using conventional sampling techniques.
Cornell University（康奈尔大学）；Samsung AI Center in Moscow（三星莫斯科人工智能中心）；Higher School of Economics（高等经济学院）；Courant Institute and Center for Data Science, New York University（纽约大学库朗研究所与数据科学中心）
Likelihood-Free Inference with Deep Gaussian Processes
Helsinki Institute for Information Technology（赫尔辛基信息技术研究所）；Aalto University（阿尔托大学）；University of Oslo（奥斯陆大学）；University of Helsinki（赫尔辛基大学）；University of Manchester（曼彻斯特大学）
PriorCVAE: scalable MCMC parameter inference with Bayesian deep generative modelling
University of Oxford（牛津大学）；Aalto University（阿尔托大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）；University of Copenhagen（哥本哈根大学）；Imperial College London（伦敦帝国学院）
University of Cambridge（剑桥大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Amsterdam（阿姆斯特丹大学）；Microsoft Research（微软研究院）；The Alan Turing Institute（艾伦·图灵研究所）
alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction
California Institute of Technology（加州理工学院）；Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；University of Waterloo（滑铁卢大学）；Harvard University（哈佛大学）；Center for Astrophysics — Harvard & Smithsonian（哈佛-史密森尼天体物理中心）
