Accelerating Bayesian Inference via Multifidelity Transport Map Coupling

Mathematical models in computational physics involve uncertain parameters that impact prediction accuracy. In turbulence modeling, this challenge is especially significant: Reynolds-averaged Navier–Stokes models, such as the Spalart–Allmaras 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 multifidelity framework that combines Markov chain Monte Carlo 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 single-fidelity methods on the challenging NACA 0012 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 multifidelity approaches significantly improve turbulence parameter calibration, paving the way for more accurate and efficient aircraft certification by analysis.