Compressed neural networks for reduced order modeling

Abstract

Reduced order modeling (ROM) techniques, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), have been widely used to analyze stationary flows. Neural networks such as autoencoders are effective to reduce the dimension of non-stationary flow, but their larger storage requirements compared to POD and DMD compromise the expectations on ROM. The present work aims at compressing the autoencoder model via two distinctively different approaches, i.e., pruning and singular value decomposition (SVD). The developed algorithm is then applied to reconstruct the flow fields of typical stationary (i.e., a laminar cylinder flow and two turbulent channel flows) and non-stationary (i.e., a laminar co-rotating vortex pair) examples. It is shown that pruning and SVD reduce the size of the autoencoder network to 6% and 3% for the two simple laminar cases (or 18% and 13%, 20%, and 10% for the two complex turbulent channel flow cases), respectively, with approximately the same order of accuracy. Therefore, the proposed autoencoders optimized by the network pruning and SVD lead to effective ROM of both stationary and non-stationary flows although they require more iterations to converge than conventional methods.