Reduced-order reconstruction and uncertainty quantification of transonic compressor flow fields

To address the high computational cost of computational fluid dynamics (CFD) and the limited availability of training samples in off-design flow-field prediction for transonic compressors, this study investigates the passage flow of a 1.5-stage transonic compressor and proposes a reduced-order modeling framework based on weighted proper orthogonal decomposition (POD) and Gaussian process regression (GPR). The proposed approach incorporates both area weighting and variable scaling to achieve a unified reduced-order representation of multi-field flow data on non-uniform grids. GPR is further employed to establish a nonlinear mapping between boundary conditions and modal coefficients, enabling rapid flow-field prediction with uncertainty quantification. The results demonstrate that, compared with standard POD, the introduction of area weighting leads to faster growth of the cumulative modal energy and higher flow field reconstruction accuracy. Moreover, the GPR model accurately predicts the dominant modal coefficients, with coefficients of determination (R2) exceeding 0.99 for the first 12 modes. For flow-field reconstruction, high-fidelity predictions are achieved using the first 16 modes, yielding overall test-set R² values above 0.98 and normalized root mean square errors of approximately 6%. In addition, the proposed method successfully captures key flow features, including corner separation and shock structures. Uncertainty analysis indicates that regions of elevated uncertainty are primarily concentrated in areas associated with shocks and boundary-layer separation, showing strong consistency with the error distribution. These findings highlight the reliability and effectiveness of the proposed approach for predicting complex compressor flows.