Comprehensive Uncertainty Quantification Method for CFD Based on Sparse Autoregressive Bayesian Batch Active Learning

　　
　　With the increasing demand for CFD simulation credibility in aerospace, marine, and related fields, quantifying the impact of multi-source uncertainties—including experimental data, model parameters, and model selection—on simulation results has become a critical challenge. Existing CFD uncertainty quantification (UQ) methods typically address only single or limited uncertainty types while neglecting coupling effects, thereby restricting their engineering applicability. Moreover, quantifying multi-source uncertainties simultaneously poses significant computational challenges. This paper proposes a comprehensive UQ framework based on Bayesian statistical theory, utilizing sparse autoregressive Bayesian batch active learning. The framework encompasses model parameter estimation, predictive uncertainty modeling, and model selection uncertainty quantification. To reduce computational costs, the framework introduces a multi-fidelity deep Bayesian autoregressive neural network for constructing CFD surrogate models, develops a two-stage training strategy based on informative priors and parameter sparsification to enhance network training efficiency, and designs a batch active learning strategy that integrates space-filling weighted maximum mutual information with determinantal point processes to optimize sample information value and spatial diversity. Validation through mathematical examples and aerodynamic analysis of the MD30P30N airfoil demonstrates that the proposed method significantly improves network training speed and reduces the overall cost of surrogate model construction compared to existing approaches, thereby efficiently achieving comprehensive multi-source uncertainty quantification and providing reliable confidence assessment for CFD engineering decisions.
　　With the increasing demand for CFD simulation credibility in aerospace, marine, and related fields, quantifying the impact of multi-source uncertainties—including experimental data, model parameters, and model selection—on simulation results has become a critical challenge. Existing CFD uncertainty quantification (UQ) methods typically address only single or limited uncertainty types while neglecting coupling effects, thereby restricting their engineering applicability. Moreover, quantifying multi-source uncertainties simultaneously poses significant computational challenges. This paper proposes a comprehensive UQ framework based on Bayesian statistical theory, utilizing sparse autoregressive Bayesian batch active learning. The framework encompasses model parameter estimation, predictive uncertainty modeling, and model selection uncertainty quantification. To reduce computational costs, the framework introduces a multi-fidelity deep Bayesian autoregressive neural network for constructing CFD surrogate models, develops a two-stage training strategy based on informative priors and parameter sparsification to enhance network training efficiency, and designs a batch active learning strategy that integrates space-filling weighted maximum mutual information with determinantal point processes to optimize sample information value and spatial diversity. Validation through mathematical examples and aerodynamic analysis of the MD30P30N airfoil demonstrates that the proposed method significantly improves network training speed and reduces the overall cost of surrogate model construction compared to existing approaches, thereby efficiently achieving comprehensive multi-source uncertainty quantification and providing reliable confidence assessment for CFD engineering decisions.