Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification: simulators are only approximations of reality, and mismatches between simulated and real data can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of real calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by real observations, without requiring explicit knowledge of the misspecification. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty calibration compared to standard SBI baselines, while remaining computationally efficient.

翻译：仿真推断（SBI）通过从模拟数据中估计复杂非线性模型的参数，正在推动实验科学的变革。然而，一个长期存在的挑战是模型失配：仿真器仅是现实的近似，模拟数据与真实数据之间的不匹配可能导致后验分布产生偏差或过度自信。我们通过引入流匹配校正后验估计（FMCPE）框架来解决这一问题，该框架利用流匹配范式，借助少量真实校准样本来优化基于仿真训练的后验估计器。我们的方法分为两个阶段：首先，利用丰富的模拟数据训练后验近似器；其次，通过流匹配将其预测结果向真实观测支持的真实后验分布迁移，且无需显式了解失配的具体形式。这一设计使FMCPE能够兼具SBI的可扩展性与对分布偏移的鲁棒性。在合成基准测试和真实数据集的实验中，我们证明所提方法能持续缓解失配效应，相较于标准SBI基线方法，在保持计算效率的同时，显著提升了推断精度与不确定性校准质量。