Modeling transient fluid simulations with proper orthogonal decomposition and machine learning

• Published in: International journal for numerical methods in fluids 2021-02, Vol.93 (2), p.396-410
• Main Authors: Ooi, Chinchun, Le, Quang Tuyen, Dao, My Ha, Nguyen, Van Bo, Nguyen, Hoang Huy, Ba, Te
• Format: Article
• Language: English
• Subjects: Coefficients; Cylinders; Decomposition; Forecasting; incompressible flow; Learning algorithms; Long short-term memory; Machine learning; Mathematical models; model reduction; Modelling; Proper Orthogonal Decomposition; reduced order modeling; Reduced order models; Regression analysis; Short term; Support vector machines
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4888

Summary In this work, we present the results obtained from integrating several machine learning (ML) models with projection‐based reduced order model for modeling the canonical case of flow past a stationary cylinder. We demonstrate how ML models can be used to model the time‐varying characteristics of the proper orthogonal decomposition (POD) coefficients, and that the locally interpolating models such as regression trees and k‐nearest neighbors seem to be better for such models than other models like support vector regression or long‐short term memory networks. In addition, our numerical experiments also show that these POD coefficients are most effectively modeled by using their own previous time values, as opposed to the inclusion of high energy POD modes. Last but not least, we demonstrate that these models, although trained on inlet velocities of 0.8, 1.0, and 1.2 m/s, can still predict the POD coefficients of flow fields for inlet velocities of 0.9 and 1.25 m/s, with root mean squared error of under 10%. In this work, we integrate several machine learning models with projection‐based reduced order model for modeling the flow past a stationary cylinder and evaluate the choice of modeling parameters and training times required to better guide future design of such hybrid models. We demonstrate how locally‐interpolating models such as regression trees and k‐nearest neighbors perform better than support vector regression or neural networks and that these models can successfully predict the POD coefficients for various inlet velocities.