Koopman dynamic-oriented deep learning for invariant subspace identification and full-state prediction of complex systems

Wu, Jiaxin; Luo, Min; Xiao, Dunhui; Pain, Christopher C.; Khoo, Boo Cheong

doi:10.1016/j.cma.2024.117071

Computer Methods in Applied Mechanics and Engineering

2024

DOI: 10.1016/j.cma.2024.117071

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Koopman dynamic-oriented deep learning for invariant subspace identification and full-state prediction of complex systems

Jiaxin Wu,

Min Luo,

Dunhui Xiao

et al.

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Invertible neural network combined with dynamic mode decomposition applied to flow field feature extraction and prediction

Hou,

Zhang,

Fang

2024

Physics of Fluids

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The prediction error of the neural network feature extraction methods based on Koopman theory is relatively high due to the non-invertibility of the observable functions. To solve this problem, a novel deep learning architecture named invertible neural network combined with dynamic mode decomposition (INN-DMD) is proposed in this work and is applied to flow field feature extraction and prediction. The INN is used as a vectorized observable function that maps the flow field snapshots from the state space to the latent space. Then, the snapshots on the latent space are decomposed and reconstructed by the DMD algorithm. The proposed method is tested by analyzing the direct simulation results of the flow around a two-dimensional (2D) cylinder at Reynolds number equal to 9×104 and the flow around a 2D NACA (National Advisory Committee for Aeronautics) 0012 airfoil at Reynolds number equal to 2×105. The proposed INN-DMD is also compared to conventional methods such as DMD and Koopman autoencoder combined with DMD (KAE-DMD). Results indicate that INN-DMD predicts the turbulent flow field dataset with greater precision and better stability, using the same number of network parameters, due to its invertibility. INN-DMD is one to two orders of magnitude more accurate than DMD and KAE-DMD using about a quarter of the computational resources, and it shows two orders of magnitude stability improvement compared to the conventional KAE method.

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Invertible neural network combined with dynamic mode decomposition applied to flow field feature extraction and prediction

Hou,

Zhang,

Fang

2024

Physics of Fluids

View full text Add to dashboard Cite

show abstract

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Koopman dynamic-oriented deep learning for invariant subspace identification and full-state prediction of complex systems

Cited by 1 publication

References 58 publications

Invertible neural network combined with dynamic mode decomposition applied to flow field feature extraction and prediction

Invertible neural network combined with dynamic mode decomposition applied to flow field feature extraction and prediction

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