Enlarging the Domain of Attraction of Local Dynamic Mode Decomposition with Control Technique: Application to Hydraulic Fracturing

Abstract

Local Dynamic Mode Decomposition with control (LDMDc) technique combines the concept of unsupervised learning and DMDc technique to extract the relevant local dynamics associated with highly nonlinear processes to build temporally local reduced-order models (ROMs). But the limited domain of attraction (DOA) of LDMDc hinders its widespread use in prediction. To systematically enlarge the DOA of the LDMDc technique, we utilize both the states of the system and the applied inputs from the data generated using multiple ‘training’ inputs. We implement a clustering strategy to divide the data into clusters, use DMDc to build multiple local ROMs, and implement the k-nearest neighbors technique to make a selection amongst the set of ROMs during prediction. The proposed algorithm is applied to hydraulic fracturing to demonstrate the enlarged DOA of the LDMDc technique.