标题： 通过多保真度传输映射耦合加速贝叶斯推断 显示英文标题

标题： Accelerating Bayesian Inference via Multi-Fidelity Transport Map Coupling

摘要： 计算物理中的数学模型包含影响预测准确性的不确定参数。 在湍流建模中，这一挑战尤为重要：雷诺平均纳维-斯托克斯（RANS）模型，如Spalart-Allmaras（SA）模型，因其速度和鲁棒性而被广泛使用，但由于模型参数不完善，常常遭受不准确性和相关不确定性的影响。 在通过分析进行飞机认证中，对这些不确定性的可靠量化变得越来越重要，因为预测的可信度至关重要。 贝叶斯推断提供了一个估计这些参数并量化输出不确定性的框架，但传统方法成本过高，尤其是在依赖高保真度模拟时。 我们通过开发一种多保真度框架来解决昂贵的贝叶斯参数估计问题，该框架将马尔可夫链蒙特卡洛（MCMC）方法与多级蒙特卡洛（MLMC）估计器结合，以高效解决反问题。 MLMC方法需要在不同保真度水平之间获得相关样本，这通过一种基于传输映射的耦合算法实现。 我们在高攻角接近失速的具有挑战性的NACA0012机翼上，与传统的单保真度方法相比，推断成本减少了50%，同时在复杂分离流动区域为模型预测提供了现实的不确定性边界。 这些结果表明，多保真度方法显著提高了湍流参数校准，为通过分析进行更准确和高效的飞机认证铺平了道路。 显示英文摘要

摘要： Mathematical models in computational physics contain uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds averaged Navier-Stokes (RANS) models, such as the Spalart-Allmaras (SA) model, are widely used for their speed and robustness but often suffer from inaccuracies and associated uncertainties due to imperfect model parameters. Reliable quantification of these uncertainties is becoming increasingly important in aircraft certification by analysis, where predictive credibility is critical. Bayesian inference provides a framework to estimate these parameters and quantify output uncertainty, but traditional methods are prohibitively expensive, especially when relying on high-fidelity simulations. We address the challenge of expensive Bayesian parameter estimation by developing a multi-fidelity framework that combines Markov chain Monte Carlo (MCMC) methods with multilevel Monte Carlo (MLMC) estimators to efficiently solve inverse problems. The MLMC approach requires correlated samples across different fidelity levels, achieved through a novel transport map-based coupling algorithm. We demonstrate a 50% reduction in inference cost compared to traditional single-fidelity methods on the challenging NACA0012 airfoil at high angles of attack near stall, while delivering realistic uncertainty bounds for model predictions in complex separated flow regimes. These results demonstrate that multi-fidelity approaches significantly improve turbulence parameter calibration, paving the way for more accurate and efficient aircraft certification by analysis.