Bridging Simulators with Conditional Optimal Transport

2025-10-28

AI Summary

This work addresses the high-fidelity transfer of unpaired physical field data across disparate simulators. We propose Conditional Optimal Transport Flow Matching (COT-FM), a method that integrates flow-based generative modeling with conditional optimal transport theory to learn a probabilistic mapping between two weak gravitational lensing simulators—Lagrangian Perturbation Theory (LPT) and N-body Particle-Mesh (PM)—without requiring paired training data. COT-FM automatically identifies the transport path minimizing structural distortion. To our knowledge, this is the first method enabling full-field, pixel-accurate correction from LPT to N-body simulations. In experiments, COT-FM significantly outperforms conventional statistics-based approaches on posterior distribution recovery and full-field physical field inference, demonstrating superior fidelity, generalizability, and physical consistency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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.

Problem

• Bridging two simulators using unpaired simulation datasets
• Learning likelihood transport between simulators via flow-based approach
• Ensuring minimal distortion of data structure through conditional optimal transport

Innovation

• Bridges simulators using unpaired datasets
• Employs Conditional Optimal Transport Flow Matching
• Learns likelihood transport via flow-based approach