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

¹ INAF – Osservatorio Astronomico di Trieste, Via Tiepolo 11, 34131 Trieste, Italy
² PPGCosmo, Universidade Federal do Espírito Santo, 29075-910 Vitória, ES, Brazil
³ Departamento de Física, Universidade Federal do Espírito Santo, 29075-910 Vitória, ES, Brazil
⁴ IFPU – Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
⁵ INFN – Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy
⁶ Dipartimento di Fisica, Sezione di Astronomia, Università di Trieste, 34143 Trieste, Italy
⁷ ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Bologna, Italy
⁸ Centro Brasileiro de Pesquisas Físicas, 22290-180 Rio de Janeiro, Brazil
⁹ Observatório do Valongo, Universidade Federal do Rio de Janeiro, 20080-090 Rio de Janeiro, RJ, Brazil

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 8 December 2025
Accepted: 6 February 2026

Abstract

Aims. We developed 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.

Methods. We constructed a pipeline utilizing cosmological N-body simulations, creating past light cones to compute convergence and shear maps. Principal component analysis (PCA) was employed for dimensionality reduction, followed by an extreme gradient boosting (XGBoost) machine learning model to interpolate magnification PDFs across a broad cosmological parameter space (Ω_m, σ₈, w, h) and redshift range (0.2 ≤ z ≤ 6). We identified the optimal number of PCA components to balance accuracy and stability.

Results. 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 confirms 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 focuses on incorporating baryonic physics through hydrodynamical simulations and expanding the training set to further enhance model accuracy and generalizability.