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

arXiv: https://arxiv.org/abs/2012.00042 · HTML: https://mlsanity.com/paper/2012.00042/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [Machine Learning and Cosmology](https://mlsanity.com/paper/2203.08056/) (2022)
- [Inferring Black Hole Properties from Astronomical Multivariate Time Series with Bayesian Attentive Neural Processes](https://mlsanity.com/paper/2106.01450/) (2021)
- [Pixelated Reconstruction of Foreground Density and Background Surface Brightness in Gravitational Lensing Systems using Recurrent Inference Machines](https://mlsanity.com/paper/2301.04168/) (2023)
- [Strong Gravitational Lensing Parameter Estimation with Vision Transformer](https://mlsanity.com/paper/2210.04143/) (2022)

## Abstract (arXiv)

We investigate the use of approximate Bayesian neural networks (BNNs) in modeling hundreds of time-delay gravitational lenses for Hubble constant (H0) 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 H0 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 H0. A simple combination of 200 test-set lenses results in a precision of 0.5 textrmkm s-1 textrm Mpc-1 (0.7%), with no detectable bias in this H0 recovery test. The computation time for the entire pipeline -- including the training set generation, BNN training, and H0 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 H0 inference.