(672g) Big Data for Enhanced Reduced Order Modeling: Application to Hydraulic Fracturing
However, the domain of attraction (DOA) of Local DMDc is narrow; meaning, it will be less accurate when used for prediction purposes under conditions outside the training data. In this work, we overcome the problem of limited DOA of Local DMDc by using multiple training data sets obtained under distinct training conditions. Specifically, training data is divided into clusters such that each cluster represents certain unique, local dynamics of the system and a DMDc-based local ROM is built for each cluster. Also, a unique identity is built for each cluster by transforming the data through normalization, applying weights, and Principal Component Analysis (PCA). The identity for each cluster is the average of the PCA scores of all the data points it contains. During prediction, given a state and input, we utilize the k-nearest neighbors (kNN) technique to select the appropriate local ROM in order to calculate the future state of the system. We demonstrate the performance of our proposed algorithm by applying it to hydraulic fracturing, a highly non-linear and complex process represented by a system of nonlinear highly-coupled PDEs with time-dependent spatial domain . We utilize its high-fidelity model to generate training data obtained by using distinct training inputs, build multiple local ROMs based on DMDc, and utilize kNN for the purposes of model selection. We demonstrate the enlarged DOA through increased applicability of the LDMDc models obtained using the proposed algorithm for a wide range of operating conditions
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