In this manuscript, we combine non-intrusive reduced order models (ROMs) with space-dependent aggregation techniques to build a mixed-ROM. The prediction of the mixed formulation is given by a convex linear combination of the predictions of some previously-trained ROMs, where we assign to each model a space-dependent weight. The ROMs taken into account to build the mixed model exploit different reduction techniques, such as Proper Orthogonal Decomposition (POD) and AutoEncoders (AE), and/or different approximation techniques, namely a Radial Basis Function Interpolation (RBF), a Gaussian Process Regression (GPR) or a feed-forward Artificial Neural Network (ANN). The contribution of each model is retained with higher weights in the regions where the model performs best, and, vice versa, with smaller weights where the model has a lower accuracy with respect to the other models. Finally, a regression technique, namely a Random Forest, is exploited to evaluate the weights for unseen conditions. The performance of the aggregated model is evaluated on two different test cases: the 2D flow past a NACA 4412 airfoil, with an angle of attack of 5 degrees, having as parameter the Reynolds number varying between 1e5 and 1e6 and a transonic flow over a NACA 0012 airfoil, considering as parameter the angle of attack. In both cases, the mixed-ROM has provided improved accuracy with respect to each individual ROM technique.

翻译：本文结合非侵入式降阶模型与空间依赖聚合技术构建混合降阶模型。混合模型通过将多个预训练降阶模型预测结果的凸线性组合进行预测，其中每个模型被赋予空间依赖权重。构建混合模型所采用的降阶模型利用不同降阶技术（如本征正交分解与自编码器）和/或不同逼近技术（即径向基函数插值、高斯过程回归或前馈人工神经网络）。各模型贡献在其表现最优区域保留较高权重，反之在相对于其他模型精度较低区域则赋予较小权重。最终采用随机森林回归技术评估未见工况下的权重。聚合模型性能通过两个测试案例进行验证：攻角5°的NACA 4412翼型二维绕流（以雷诺数在1e5至1e6范围内变化为参数）以及NACA 0012翼型跨音速流动（以攻角为参数）。两种情况下，混合降阶模型相比各单独降阶技术均展现出更高的预测精度。