Accelerating Bayesian Inference via Multi-Fidelity Transport Map Coupling

TL;DR

This paper introduces a multi-fidelity Bayesian inference framework using transport map coupling to efficiently calibrate turbulence model parameters, significantly reducing computational costs while maintaining accurate uncertainty quantification.

Contribution

It develops a novel transport map-based coupling algorithm for multi-fidelity MCMC, enabling efficient Bayesian parameter estimation in complex turbulence models.

Findings

50% reduction in inference cost compared to single-fidelity methods

Achieved realistic uncertainty bounds in complex flow regimes

Demonstrated effectiveness on NACA0012 airfoil at high angles of attack

Abstract

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.