Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low dimensionalization

Morimoto, Masaki; Fukami, Kai; Zhang, Kai; Nair, Aditya; Fukagata, Koji

doi:10.1007/s00162-021-00580-0

Cited by 73 publications

(35 citation statements)

References 65 publications

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“…One of the issues associated with the MLP is that the number of edges inside it may explode due to its fully-connected structure when handling high-dimensional data such as fluid flows. To overcome this issue in dealing with fluid flow problems, a convolutional neural network (CNN) 19 has widely been accepted as a good candidate 3 , 20 . We capitalize on the combination of two- and three-dimensional CNNs for the state estimation task in the present study.…”

Section: Regression Methodsmentioning

confidence: 99%

Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions

Nakamura

Fukami

Fukagata

2022

Sci Rep

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Neural networks (NNs) and linear stochastic estimation (LSE) have widely been utilized as powerful tools for fluid-flow regressions. We investigate fundamental differences between them considering two canonical fluid-flow problems: (1) the estimation of high-order proper orthogonal decomposition coefficients from low-order their counterparts for a flow around a two-dimensional cylinder, and (2) the state estimation from wall characteristics in a turbulent channel flow. In the first problem, we compare the performance of LSE to that of a multi-layer perceptron (MLP). With the channel flow example, we capitalize on a convolutional neural network (CNN) as a nonlinear model which can handle high-dimensional fluid flows. For both cases, the nonlinear NNs outperform the linear methods thanks to nonlinear activation functions. We also perform error-curve analyses regarding the estimation error and the response of weights inside models. Our analysis visualizes the robustness against noisy perturbation on the error-curve domain while revealing the fundamental difference of the covered tools for fluid-flow regressions.

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Section: Regression Methodsmentioning

confidence: 99%

Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions

Nakamura

Fukami

Fukagata

2022

Sci Rep

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“…The present CNN is composed of convolutional layers, which allows us to extract spatial coherent features of data through filter operations. Note that pooling or upsampling operations are not considered in the present study because no dimension reduction or expansion is required for the present model such that R 𝑑 input = R 𝑑 output , where 𝑑 input and 𝑑 output denote the vector dimensions of input and output data, respectively (Morimoto et al, 2021c). The operation at the 𝑠-th convolutional layer 𝑞 (𝑠) can mathematically be expressed as…”

Section: Convolutional Neural Network-based State Estimator For Fluid...mentioning

confidence: 99%

Robust training approach of neural networks for fluid flow state estimations

Nakamura,

Fukagata

2021

Preprint

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State estimation from limited sensor measurements is ubiquitously found as a common challenge in a broad range of fields including mechanics, astronomy, and geophysics. Fluid mechanics is no exception -state estimation of fluid flows is particularly important for flow control and processing of experimental data. However, strong nonlinearities and spatio-temporal high degrees of freedom of fluid flows cause difficulties in reasonable estimations. To handle these issues, neural networks (NNs) have recently been applied to the fluid flow estimation instead of conventional linear methods. The present study focuses on the capability of NNs to various fluid flow estimation problems from a practical viewpoint regarding robust training. Three types of unsteady laminar and turbulent flows are considered for the present demonstration: 1. square cylinder wake, 2. turbulent channel flow, and 3. laminar to turbulent transitional boundary layer. We utilize a convolutional neural network (CNN) to estimate velocity fields from sectional sensor measurements. To assess the practicability of the CNN models, physical quantities required for the input and robustness against lack of sensors are investigated. We also examine the effectiveness of several considerable approaches for model training to gain more robustness against the lack of sensors. The knowledge acquired through the present study in terms of effective training approaches can be transferred towards practical machine learning in fluid flow modeling.

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“…SWAG relies on estimating weight distributions for arbitrary neural-network architectures. To demonstrate this, we consider two types of architectures: (i) MLP-CNN-based estimator [74,75,76] and (ii) CNN [14,18,77,78]. These two examples have respectively been used for a broad range of fluid-flow approximations.…”

Section: Machine-learning Modelsmentioning

confidence: 99%

Assessments of model-form uncertainty using Gaussian stochastic weight averaging for fluid-flow regression

Morimoto,

Fukami,

Maulik

et al. 2021

Preprint

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We use Gaussian stochastic weight averaging (SWAG) to assess the model-form uncertainty associated with neural-network-based function approximation relevant to fluid flows. SWAG approximates a posterior Gaussian distribution of each weight, given training data, and a constant learning rate. Having access to this distribution, it is able to create multiple models with various combinations of sampled weights, which can be used to obtain ensemble predictions. The average of such an ensemble can be regarded as the 'mean estimation', whereas its standard deviation can be used to construct 'confidence intervals', which enable us to perform uncertainty quantification (UQ) with regard to the training process of neural networks. We utilize representative neural-network-based function approximation tasks for the following cases: (i) a two-dimensional circular-cylinder wake; (ii) the DayMET dataset (maximum daily temperature in North America); (iii) a three-dimensional square-cylinder wake; and (iv) urban flow, to assess the generalizability of the present idea for a wide range of complex datasets. SWAG-based UQ can be applied regardless of the network architecture, and therefore, we demonstrate the applicability of the method for two types of neural networks: (i) global field reconstruction from sparse sensors by combining convolutional neural network (CNN) and multi-layer perceptron (MLP); and (ii) far-field state estimation from sectional data with two-dimensional CNN. We find that SWAG can obtain physically-interpretable confidence-interval estimates from the perspective of model-form uncertainty. This capability supports its use

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Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low dimensionalization

Cited by 73 publications

References 65 publications

Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions

Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions

Robust training approach of neural networks for fluid flow state estimations

Assessments of model-form uncertainty using Gaussian stochastic weight averaging for fluid-flow regression

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