大尺度引力透镜的贝叶斯神经网络建模及其哈勃常数的精确推断
Large-Scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant
摘要：
我们研究了使用近似贝叶斯神经网络（BNN）在数百个时延引力透镜的哈勃常数（$H_0$）的测定建模。我们的BNN是在包含透镜星系光的强透镜活动星系核（AGN）的合成HST质量图像上训练的。该神经网络能够准确地表征外剪切场中椭圆幂律质量分布模型参数的后验概率密度函数。然后，我们传播的BNN推断后PDF集成$H_0$推理，使用模拟的时间延迟测量从一个合理的专用监测活动。假设测量良好的时间延迟和一组合理的先验的环境中的镜头，我们实现了$9.3$\ %的中位数精度每个镜头中推断的$H_0$。200个试验组镜片的简单组合可获得0.5 $\textrm{km s}^{-1} \textrm{ Mpc}^{-1}$（$0.7\%$）的精密度，在该$H_0$回收试验中未检测到偏倚。整个流水线的计算时间-包括训练集生成、BNN训练和$H_0$推断-对于200个镜片，平均每个镜片转换为9分钟，随着样本量的增加，每个镜片收敛为6分钟。由于完全自动化和高效，我们的管道是一个有前途的工具，探索合奏级系统的镜头建模$H_0$推理。
英文摘要：
We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time-delay gravitational lenses for Hubble constant ($H_0$) determination. Our BNN was trained on synthetic HST-quality images of strongly lensed active galactic nuclei (AGN) with lens galaxy light included. The BNN can accurately characterize the posterior PDFs of model parameters governing the elliptical power-law mass profile in an external shear field. We then propagate the BNN-inferred posterior PDFs into ensemble $H_0$ inference, using simulated time delay measurements from a plausible dedicated monitoring campaign. Assuming well-measured time delays and a reasonable set of priors on the environment of the lens, we achieve a median precision of $9.3$\% per lens in the inferred $H_0$. A simple combination of 200 test-set lenses results in a precision of 0.5 $\textrm{km s}^{-1} \textrm{ Mpc}^{-1}$ ($0.7\%$), with no detectable bias in this $H_0$ recovery test. The computation time for the entire pipeline -- including the training set generation, BNN training, and $H_0$ inference -- translates to 9 minutes per lens on average for 200 lenses and converges to 6 minutes per lens as the sample size is increased. Being fully automated and efficient, our pipeline is a promising tool for exploring ensemble-level systematics in lens modeling for $H_0$ inference.
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