Cascade neural network model for predicting the flow field of two-dimensional nozzle with data assimilation

This is new, This study presents a cascaded neural network framework for predicting internal flow fields in two-dimensional vectoring nozzles by integrating computational fluid dynamics (CFD) simulations with sparse experimental data. The framework consists of two core models: a one-dimensional convolutional Pressure Scan Network (PSnet) and a U-Net-based Contour Reconstruction Network (CRnet). In the test set evaluation, PSnet predicts wall pressure distributions from geometric parameters with a mean absolute error (MAE) of 0.005, accurately capturing shock locations and pressure gradients. CRnet reconstructs two-dimensional flow contours from wall pressure and geometry-derived features, achieving a mean relative error (MRE) of 0.001 and a structural similarity index (SSIM) of 0.948, thereby demonstrating strong accuracy in recovering detailed flow structures such as shocks and expansion waves. A data assimilation method is further employed to incorporate sparse experimental pressure measurements, reducing prediction errors by up to 34 % on average across the test set. Results from the ablation and robustness studies confirm that the proposed input configuration and training strategy are not only effective but also essential for accurate flow field reconstruction. Overall, the cascaded framework provides an efficient and accurate surrogate modeling approach, enabling flow field prediction from design parameters and facilitating the practical integration of limited experimental data into the aerodynamic design process.