Accurate cosmological emulator for the probability distribution function of gravitational lensing of point sources

TL;DR

This paper presents a fast, accurate emulator for the gravitational lensing magnification PDF, enabling improved cosmological inference from point sources like supernovae and gravitational waves.

Contribution

The authors develop a machine learning-based emulator using PCA and XGBoost trained on N-body simulations to model lensing PDFs across cosmological parameters and redshifts.

Findings

Emulator achieves median KL divergence of 0.007, indicating high accuracy.

Reliable reproduction of PDF shapes and statistical properties across parameter space.

Validated across various redshifts and cosmological models.

Abstract

We develop an accurate and computationally efficient emulator to model the gravitational lensing magnification probability distribution function (PDF), enabling robust cosmological inference of point sources such as supernovae and gravitational-wave observations. We construct a pipeline utilizing cosmological $N$-body simulations, creating past light cones to compute convergence and shear maps. Principal Component Analysis (PCA) is employed for dimensionality reduction, followed by an eXtreme Gradient Boosting (XGBoost) machine learning model to interpolate magnification PDFs across a broad cosmological parameter space ($\Omega_m$, $\sigma_8$, $w$, $h$) and redshift range ($0.2 \le z \le 6$). We identify the optimal number of PCA components to balance accuracy and stability. Our emulator, publicly released as ace_lensing, accurately reproduces lensing PDFs with a median Kullback-Leibler divergence of $0.007$. Validation on the test set confirmed that the model reliably reproduces the detailed shapes and statistical properties of the PDFs across the explored parameter range, showing no significant degradation for specific parameter combinations or redshifts. Future work will focus on incorporating baryonic physics through hydrodynamical simulations and expanding the training set to further enhance model accuracy and generalizability.