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Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes

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Abstract

We propose a method to construct a reduced order model with machine learning for unsteady flows. The present machine-learned reduced order model (ML-ROM) is constructed by combining a convolutional neural network autoencoder (CNN-AE) and a long short-term memory (LSTM), which are trained in a sequential manner. First, the CNN-AE is trained using direct numerical simulation (DNS) data so as to map the high-dimensional flow data into low-dimensional latent space. Then, the LSTM is utilized to establish a temporal prediction system for the low-dimensionalized vectors obtained by CNN-AE. As a test case, we consider flows around a bluff body whose shape is defined using a combination of trigonometric functions with random amplitudes. The present ML-ROMs are trained on a set of 80 bluff body shapes and tested on a different set of 20 bluff body shapes not used for training, with both training and test shapes chosen from the same random distribution. The flow fields are confirmed to be well reproduced by the present ML-ROM in terms of various statistics. We also focus on the influence of two main parameters: (1) the latent vector size in the CNN-AE, and (2) the time step size between the mapped vectors used for the LSTM. The present results show that the ML-ROM works well even for unseen shapes of bluff bodies when these parameters are properly chosen, which implies great potential for the present type of ML-ROM to be applied to more complex flows.

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Acknowledgements

Authors are grateful to Dr. S. Obi, Dr. K. Ando, Mr. M. Morimoto, and Mr. T. Nakamura (Keio University) for fruitful discussions. This work was supported through JSPS KAKENHI Grant Number 18H03758 by Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan

    Kazuto Hasegawa, Kai Fukami, Takaaki Murata & Koji Fukagata

  2. Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, 20156, Milan, Italy

    Kazuto Hasegawa

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  1. Kazuto Hasegawa
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  2. Kai Fukami
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Correspondence to Koji Fukagata.

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Communicated by Kunihiko Taira.

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Hasegawa, K., Fukami, K., Murata, T. et al. Machine-learning-based reduced-order modeling for unsteady flows around bluff bodies of various shapes. Theor. Comput. Fluid Dyn. 34, 367–383 (2020). https://doi.org/10.1007/s00162-020-00528-w

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