Error estimation of the parametric non-intrusive reduced order model using machine learning

Abstract A novel error estimation method for the parametric non-intrusive reduced order model (P-NIROM) based on machine learning is presented. This method relies on constructing a set of response functions for the errors between the high fidelity full model solutions and P-NIROM using machine learning method, particularly, Gaussian process regression method. This yields closer solutions agreement with the high fidelity full model. The novelty of this work is that it is the first time to use machine learning method to derive error estimate for the P-NIROM. The capability of the new error estimation method is demonstrated using three numerical simulation examples: flow past a cylinder, dam break and 3D fluvial channel. It is shown that the results are closer to those of the high fidelity full model when considering error terms. In addition, the interface between two phases of dam break case is captured well if the error estimator is involved in the P-NIROM.

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