[Paper Review] Simulation-Based Inference of Strong Gravitational Lensing Parameters

Ronan Legin, Yashar Hezaveh+2 more|arXiv (Cornell University)|Dec 10, 2021

Pulsars and Gravitational Waves Research4 citations

TL;DR

This paper proposes a simulation-based inference framework using density estimation to enable accurate, fast, and calibrated posterior inference for strong gravitational lensing parameters. By leveraging compressed statistics from approximate Bayesian neural networks as inputs to a mixture density network, the method achieves well-calibrated posteriors without hyperparameter tuning, enabling efficient posterior estimation for hundreds of thousands of lenses.

ABSTRACT

In the coming years, a new generation of sky surveys, in particular, Euclid Space Telescope (2022), and the Rubin Observatory's Legacy Survey of Space and Time (LSST, 2023) will discover more than 200,000 new strong gravitational lenses, which represents an increase of more than two orders of magnitude compared to currently known sample sizes. Accurate and fast analysis of such large volumes of data under a statistical framework is therefore crucial for all sciences enabled by strong lensing. Here, we report on the application of simulation-based inference methods, in particular, density estimation techniques, to the predictions of the set of parameters of strong lensing systems from neural networks. This allows us to explicitly impose desired priors on lensing parameters, while guaranteeing convergence to the optimal posterior in the limit of perfect performance.

Motivation & Objective

• To address the critical need for accurate, scalable, and uncertainty-quantified inference of strong lensing parameters in the era of large sky surveys.
• To overcome limitations of approximate Bayesian neural networks, which lack explicit prior control and suffer from unquantifiable approximations.
• To develop a method that guarantees convergence to the true posterior under perfect performance while allowing explicit prior specification.
• To enable efficient posterior estimation for tens of thousands of lenses using minimal computational resources.
• To provide a framework that is robust to real-world observational effects such as stellar light from lenses by incorporating them into simulations.

Proposed method

• Compressed statistics are extracted from approximate Bayesian neural networks (BNNs) by computing the mean of predicted posterior distributions over lensing parameters.
• The BNNs use variational inference with dropout to model uncertainty, where dropout is applied to network weights to approximate posterior distributions.
• A mixture density network (MDN) is trained to model the likelihood of the compressed statistics given the true lensing parameters, enabling density estimation of the posterior.
• The MDN learns the mapping from image data to a full posterior distribution over lensing parameters, using simulated lensing images and their true parameters as training data.
• Posterior coverage is validated using coverage probability tests, ensuring that true parameters are consistently within predicted credible intervals.
• The method is computationally efficient, enabling posterior sampling for 10,000 lenses in ~20 minutes using a single GPU.

Experimental results

Research questions

• RQ1 Can simulation-based inference with density estimation provide well-calibrated posteriors for strong lensing parameters without requiring hyperparameter tuning?
• RQ2 Can compressed statistics derived from Bayesian neural networks be effectively used to train a density estimator that recovers the true posterior distribution?
• RQ3 Does the method maintain accuracy when the BNNs used for compression include dropout-induced noise?
• RQ4 How does the method perform under realistic observational effects such as stellar light from the lens galaxy?
• RQ5 Can the framework be extended to handle complex source morphologies beyond the Sersic model?

Key findings

• The method achieves well-calibrated posterior coverage without any hyperparameter tuning, indicating reliable uncertainty quantification.
• Posterior samples generated using the MDN-based likelihood show accurate coverage probabilities, confirming convergence to the true posterior under ideal conditions.
• The performance of the MDN is comparable whether trained on compressed statistics from BNNs with 0% or 20% dropout, suggesting robustness to noise from dropout.
• The framework enables posterior inference for 10,000 lensing simulations in approximately 20 minutes using a single NVIDIA V100 GPU, demonstrating high computational efficiency.
• The approach is extensible to real-world complexities, such as foreground stellar light, by including them in the simulation pipeline, ensuring robustness to observational artifacts.
• Future evaluation using the multidimensional Kolmogorov-Smirnov test will further validate the method’s ability to produce statistically valid posteriors across high-dimensional parameter spaces.