标题： 基于贝叶斯神经网络的大规模引力透镜建模用于哈勃常数的准确和精确推断 显示英文标题

标题： Large-Scale Gravitational Lens Modeling with Bayesian Neural Networks for Accurate and Precise Inference of the Hubble Constant

摘要： 我们研究了近似贝叶斯神经网络（BNN）在建模数百个时滞引力透镜以确定哈勃常数（$H_0$）中的应用。 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。 BNN可以准确表征控制外部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，我们使用从一个合理的专门监测计划中模拟的时间延迟测量值，将BNN推断的后验概率密度函数传播到集合$H_0$推断中。 假设时间延迟测量良好，并且透镜环境有一组合理先验，我们在推断的$H_0$中每透镜实现了中位精度$9.3$%。 200个测试集透镜的简单组合结果实现了0.5$\textrm{km s}^{-1} \textrm{ Mpc}^{-1}$（$0.7\%$）的精度，在此$H_0$恢复测试中没有检测到偏差。 整个流程的计算时间——包括训练集生成、BNN 训练和$H_0$推理——平均为每个透镜 9 分钟，针对 200 个透镜，当样本量增加时，收敛到每个透镜 6 分钟。 由于完全自动化且高效，我们的流程是探索$H_0$推理中集合级系统误差的有前途的工具。 显示英文摘要

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.