Bridging Simulators with Conditional Optimal Transport

TL;DR

This paper introduces a flow-based emulator that uses Conditional Optimal Transport Flow Matching to accurately bridge different simulation models, enabling precise full-field inference without paired datasets.

Contribution

It presents a novel method combining flow-based transport and COT-FM to connect unpaired simulators, improving the accuracy of simulation-based inference.

Findings

Successfully bridges weak lensing simulators (LPT to N-body PM)

Enables full-field inference with accurate posterior recovery

Outperforms traditional summary statistic methods

Abstract

We propose a new field-level emulator that bridges two simulators using unpaired simulation datasets. Our method leverages a flow-based approach to learn the likelihood transport from one simulator to the other. Since multiple transport maps exist, we employ Conditional Optimal Transport Flow Matching (COT-FM) to ensure that the transformation minimally distorts the underlying structure of the data. We demonstrate the effectiveness of this approach by bridging weak lensing simulators: a Lagrangian Perturbation Theory (LPT) to a N-body Particle-Mesh (PM). We demonstrate that our emulator captures the full correction between the simulators by showing that it enables full-field inference to accurately recover the true posterior, validating its accuracy beyond traditional summary statistics.