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Time–space coupled learning method for model reduction of distributed parameter systems with encoder‐decoder and RNN
Author(s) -
Qing Xiangyun,
Jin Jing,
Niu Yugang,
Zhao Shuangliang
Publication year - 2020
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.16251
Subject(s) - dimensionality reduction , reduction (mathematics) , encoder , computer science , recurrent neural network , dimension (graph theory) , curse of dimensionality , deep learning , coupling (piping) , algorithm , control theory (sociology) , space (punctuation) , artificial neural network , artificial intelligence , mathematics , engineering , control (management) , mechanical engineering , geometry , pure mathematics , operating system
Model reduction of a high‐dimensional distributed parameter system (DPS) reduces the complexity of the system for various applications, from monitoring to model predictive control, while retaining its intrinsic properties. Unfortunately, the assumption of time–space separability usually fails to hold for popular time–space separation model reduction methods because the space and time of the DPS are inherently coupled. In this study, a time–space coupled learning method for a data‐driven model reduction of the DPS is presented. The proposed method has the advantage of preserving the time–space coupling characteristics and increasing the number of degrees of freedom during the model reduction learning process. A novel deep‐learning architecture is presented by combining encoder‐decoder networks with recurrent neural networks. Given a high‐dimensional system without an exact partial differential equation description, the dimension‐reduced model and its temporal dynamics are jointly learned using the collected input and output data. The learned model is then applied to predict the low‐dimensional representations and reconstruct the high‐dimensional outputs. The proposed method was demonstrated on the catalytic rod in a tubular reactor with recycle, the results of which indicate a better modeling accuracy and lower intrinsic dimensionality compared with classical time–space separation model reduction methods.