FLUMEN: Neural Emulator of an Advanced Stochastic Weak Lensing Model

Weak gravitational lensing by intervening structure magnifies distant sources and induces scatter in their luminosity distances. We develop an improved stochastic model for the distribution of weak lensing magnifications, $\text{d}P\mathrm{/}\text{d}\mu$, that resolves individual lenses down to ${10}^7{M}_{\odot }$ and, besides field halos and filaments, includes subhalos and large-scale clustering of the lens population. Both extensions broaden the distribution, and the resulting scatter in the luminosity distances agrees with the halo-model prediction from the nonlinear matter power spectrum and exceeds that obtained from $N$-body ray tracing, which we attribute to the finite mass resolution and box size of the simulations. Building on this model, we develop $\mathtt{\text{FLUMEN}}$, a conditional normalizing-flow emulator that predicts $\text{d}P\mathrm{/}\text{d}\mu$ as a function of the source redshift up to $z_s=12$ and six cosmological parameters $\{h,{\mathrm{\Omega }}_M,{\mathrm{\Omega }}_B,{\sigma }_8,n_s,z_{\mathrm{e}\mathrm{q}}\}$. The emulator enforces the empty-beam cutoff and the fold-caustic power-law tail analytically, and reproduces the Monte Carlo distributions on held-out cosmologies with a median Kullback–Leibler divergence of $0.0048$ at negligible cost. Our results provide a fast and flexible framework for incorporating the full magnification distribution into cosmological analyses of standard sirens, supernovae, and other point sources.