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

TL;DR

The paper introduces ace_lensing, an emulator for the gravitational lensing magnification PDF built from a pipeline of nonlinear $N$-body simulations and past-light-cone maps. It uses PCA to compress PDFs and XGBoost to interpolate across the cosmological parameters $(\Omega_m,\sigma_8,w,h)$ and redshift range $0.2 \le z \le 6$. The emulator achieves a median $D_{\rm KL}$ of about $0.007$ on a test set, faithfully reproducing PDF shapes and moments across the parameter space. The authors publicly release the code and plan to include hydrodynamical effects and larger training sets to improve accuracy and generalization.

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 ($Ω_m$, $σ_8$, $w$, $h$) 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.

Figures (18)

• Figure 1: Distribution of the values of the cosmological parameters for the 70 cosmologies here employed to build the lensing PDF emulator. These values were generated via Latin hypercube sampling.
• Figure 2: Comparison between the matter power spectrum measured from the simulation snapshots and the nonlinear prediction from baccoemu.
• Figure 3: Redshift dependence of resolvable matter fluctuations. The dots show the scale at which density fluctuations reach unity ($\sigma_R = 1$), and the black dashed line indicates the simulation’s mean particle separation. Regions below the dashed line are not reliably captured by the simulation due to resolution limits.
• Figure 4: Convergence root mean square as a function of grid size, used to determine the optimal resolution before entering the shot-noise dominated regime. The chosen optimal value (12 kpc/h) balances noise and resolution.
• Figure 5: KL divergence between original and reconstructed PDFs as a function of the number of PCA components. Error bars indicate the 16th–84th percentile range across 1447 PDFs.