Enhancing non-intrusive Reduced Order Models with space-dependent aggregation methods
arxiv(2024)
摘要
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.
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