Accelerating Bayesian Inference via Multi-Fidelity Transport Map Coupling

2025-10-20

AI Summary

Turbulence model parameters—e.g., in the Spalart–Allmaras RANS model—exhibit significant uncertainty, undermining aerodynamic prediction reliability and limiting applicability in high-assurance contexts such as aircraft certification. Conventional Bayesian inversion can quantify both parameter and predictive uncertainties but incurs prohibitive computational cost due to its reliance on high-fidelity simulations. This paper proposes a multifidelity Bayesian inversion framework that innovatively integrates Markov chain Monte Carlo (MCMC), multilevel Monte Carlo (MLMC), and transport-map-based strongly coupled sampling to enhance correlation across fidelity levels. Validated on separated flow over the NACA0012 airfoil at high angles of attack, the method reduces inference cost by 50% while yielding more physically consistent uncertainty bounds. Consequently, calibration efficiency and predictive credibility are simultaneously improved.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User model development and evaluation
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Accelerating expensive Bayesian inference for turbulence modeling
• Reducing computational cost of parameter uncertainty quantification
• Improving aircraft certification via multi-fidelity calibration methods

Innovation

• Multi-fidelity framework combining MCMC and MLMC
• Transport map-based coupling for correlated samples
• Reduced inference cost by 50% for turbulence calibration