Bridging Simulators with Conditional Optimal Transport

Abstract

Weak lensing convergence maps are expected to be significantly non-Gaussian on small scales, causing the power spectrum to fail as a sufficient statistic for cosmological parameters by discarding information encoded in higher-order correlations. This limitation is particularly pressing in the context of next-generation surveys, which will improve the signal-to-noise ratio and grant access to deeply non-linear scales. To tighten constraints on cosmological parameters, neural-network-based full-field inference methods have recently emerged as a promising avenue; however, they require large suites of computationally expensive simulations. To address this challenge, we propose a new approach to building pixel-level emulators (Zeghal et al., 2025). By learning a minimal conditional transformation between cheap and costly simulations using Conditional Optimal Transport Flow Matching (COT-FM, Kerrigan et al., 2024), we show that we can generate new high-fidelity simulations whose statistics match those of the expensive simulator across cosmological parameters. We validate this by performing full-field inference on the emulated simulations and demonstrate that the resulting posteriors are in excellent agreement with those obtained from the true costly simulations. Notably, our emulator can operate on unpaired datasets. This flexibility enabled us to secure second place in the Weak Lensing Uncertainty Challenge at NeurIPS 2025, where only the simulations and their corresponding cosmological parameters were provided, without access to the initial conditions needed to pair them with their cheap counterparts.