Flow Matching for Simulation-Based Inference: Design Choices and Implications

Authors

Massimiliano Giordano Orsini, Alessio Ferone, Laura Inno, Angelo Casolaro, Antonio Maratea

Abstract

Inverse problems are ubiquitous across many scientific fields, and involve the determination of the causes or parameters of a system from observations of its effects or outputs. These problems have been deeply studied through the use of simulated data, thereby under the lens of simulation-based inference. Recently, the natural combination of Continuous Normalizing Flows (CNFs) and Flow Matching Posterior Estimation (FMPE) has emerged as a novel, powerful, and scalable posterior estimator, capable of inferring the distribution of free parameters in a significantly reduced computational time compared to conventional techniques. While CNFs provide substantial flexibility in designing machine learning solutions, modeling decisions during their implementation can strongly influence predictive performance. To the best of our knowledge, no prior work has systematically analyzed how such modeling choices affect the robustness of posterior estimates in this framework. The aim of this work is to address this research gap by investigating the sensitivity of CNFs trained with FMPE under different modeling decisions, including data preprocessing, noise conditioning, and noisy observations. As a case study, we consider atmospheric retrieval of exoplanets and perform an extensive experimental campaign on the Ariel Data Challenge 2023 dataset. Through a comprehensive posterior evaluation framework, we demonstrate that (i) Z-score normalization outperforms min–max scaling across tasks; (ii) noise conditioning improves accuracy, coverage, and uncertainty estimation; and (iii) noisy observations significantly degrade predictive performance, thus underscoring reduced robustness under the assumed noise conditions.