Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows

Fukami, Kai; Fukagata, Koji; Taira, Kunihiko

doi:10.1017/jfm.2020.948

Cited by 171 publications

(90 citation statements)

References 44 publications

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“…2019 c ; Fukami, Fukagata & Taira 2020 a ; Fukami et al. 2021 b ; Omata & Shirayama 2019; Morimoto, Fukami & Fukagata 2020 a ; Fukami, Fukagata & Taira 2021 a ; Matsuo et al. 2021; Morimoto et al.…”

Section: Methodsmentioning

confidence: 99%

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

et al. 2021

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We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm and the adaptive least absolute shrinkage and selection operator which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at $Re_D=100$ , its transient process and a wake of two-parallel cylinders, as examples of high-dimensional fluid data. To handle these high-dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized. The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space. The SINDy then seeks a governing equation of the mapped low-dimensional latent vector. Temporal evolution of high-dimensional dynamics can be provided by combining the predicted latent vector by SINDy with the CNN decoder which can remap the low-dimensional latent vector to the original dimension. The SINDy can provide a stable solution as the governing equation of the latent dynamics and the CNN-SINDy-based modelling can reproduce high-dimensional flow fields successfully, although more terms are required to represent the transient flow and the two-parallel cylinder wake than the periodic shedding. A nine-equation turbulent shear flow model is finally considered to examine the applicability of SINDy to turbulence, although without using CNN-AE. The present results suggest that the proposed scheme with an appropriate parameter choice enables us to analyse high-dimensional nonlinear dynamics with interpretable low-dimensional manifolds.

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Section: Methodsmentioning

confidence: 99%

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

et al. 2021

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“…In recent years, machine learning methods have exemplified their great potential in fluid dynamics, e.g., turbulence modeling [17][18][19][20][21][22][23][24][25], and spatio-temporal data estimation [26][27][28][29][30][31][32][33][34][35][36][37]. Reduced order modeling (ROM) is no exception, referred to as machine-learning-based ROM (ML-ROM).…”

Section: Introductionmentioning

confidence: 99%

Model Order Reduction with Neural Networks: Application to Laminar and Turbulent Flows

et al. 2021

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We investigate the capability of neural network-based model order reduction, i.e., autoencoder (AE), for fluid flows. As an example model, an AE which comprises of convolutional neural networks and multi-layer perceptrons is considered in this study. The AE model is assessed with four canonical fluid flows, namely: (1) two-dimensional cylinder wake, (2) its transient process, (3) NOAA sea surface temperature, and (4) a cross-sectional field of turbulent channel flow, in terms of a number of latent modes, the choice of nonlinear activation functions, and the number of weights contained in the AE model. We find that the AE models are sensitive to the choice of the aforementioned parameters depending on the target flows. Finally, we foresee the extensional applications and perspectives of machine learning based order reduction for numerical and experimental studies in the fluid dynamics community.

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“…Neural networks are known to be capable of extracting patterns in high-dimensional spaces and therefore have been successfully used in various studies using fluid flow data (Lee & You 2019;Kim & Lee 2020;Fukami, Fukagata & Taira 2021). Jouybari et al (2021) developed a multilayer perceptron (MLP) type neural network to find a mapping of 17 different rough surface statistics to equivalent sand-grain height.…”

Section: Introductionmentioning

confidence: 99%

Predicting drag on rough surfaces by transfer learning of empirical correlations

et al. 2021

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Recent developments in neural networks have shown the potential of estimating drag on irregular rough surfaces. Nevertheless, the difficulty of obtaining a large high-fidelity dataset to train neural networks is deterring their use in practical applications. In this study, we propose a transfer learning framework to model the drag on irregular rough surfaces even with a limited amount of direct numerical simulations. We show that transfer learning of empirical correlations, reported in the literature, can significantly improve the performance of neural networks for drag prediction. This is because empirical correlations include ‘approximate knowledge’ of the drag dependency in high-fidelity physics. The ‘approximate knowledge’ allows neural networks to learn the surface statistics known to affect drag more efficiently. The developed framework can be applied to applications where acquiring a large dataset is difficult but empirical correlations have been reported.

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Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows

Abstract: Abstract

Cited by 171 publications

References 44 publications

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

Sparse identification of nonlinear dynamics with low-dimensionalized flow representations

Model Order Reduction with Neural Networks: Application to Laminar and Turbulent Flows

Predicting drag on rough surfaces by transfer learning of empirical correlations

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