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

Kavli Affiliate: Philip J. Marshall

| First 5 Authors: Ji Won Park, Sebastian Wagner-Carena, Simon Birrer, Philip J. Marshall, Joshua Yao-Yu Lin

| Summary:

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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