Local non-intrusive reduced order modeling based on soft clustering and classification algorithm

The use of non-intrusive reduced order modeling (NIROM) to approximate high-fidelity computer models has been steadily increased over the past decade. Recently, local NIROM has been proposed to improve the model accuracy in highly nonlinear problems in which distinct characteristic regimes coexist. The core concept of local NIROM is the decomposition of the parameter domains into a subregime to create multiple models. However, the existing local NIROM not only partitions the individual models in a mutually exclusive manner, but also uses a single model for prediction. This results in the extrapolation of surrogate models and the generation of artificial discontinuities. To mitigate these problems, a local NIROM that allows flexible overlapping of individual NIROMs is developed. This method softly partitions and combines individual NIROMs using machine learning techniques, such as fuzzy c-means and multinomial logistic regression. Furthermore, a variance-based adaptive sampling technique that can consider both local exploitation and global exploration is applied to improve model accuracy. The proposed method is validated against the transonic flow and in-flight icing problem, and demonstrates superior performance relative to its local counterpart by up to 16.5% and 33.9% in terms of normalized root-mean-square error and exclusive OR error, respectively.