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

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 coe...

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Autores principales: Nakamura, Taichi, Fukami, Kai, Fukagata, Koji
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8904624/
https://www.ncbi.nlm.nih.gov/pubmed/35260621
http://dx.doi.org/10.1038/s41598-022-07515-7
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author Nakamura, Taichi
Fukami, Kai
Fukagata, Koji
author_facet Nakamura, Taichi
Fukami, Kai
Fukagata, Koji
author_sort Nakamura, Taichi
collection PubMed
description 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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spelling pubmed-89046242022-03-09 Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions Nakamura, Taichi Fukami, Kai Fukagata, Koji Sci Rep Article 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. Nature Publishing Group UK 2022-03-08 /pmc/articles/PMC8904624/ /pubmed/35260621 http://dx.doi.org/10.1038/s41598-022-07515-7 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Nakamura, Taichi
Fukami, Kai
Fukagata, Koji
Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
title Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
title_full Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
title_fullStr Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
title_full_unstemmed Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
title_short Identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
title_sort identifying key differences between linear stochastic estimation and neural networks for fluid flow regressions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8904624/
https://www.ncbi.nlm.nih.gov/pubmed/35260621
http://dx.doi.org/10.1038/s41598-022-07515-7
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