Model order reduction with neural networks: Application to laminar and turbulent flows

Fukami, Kai; Hasegawa, Kazuto; Nakamura, Taichi; Morimoto, Masaki; Fukagata, Koji

doi:10.48550/arxiv.2011.10277

Cited by 5 publications

(9 citation statements)

References 67 publications

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“…One of them is an application to turbulence, although this is extremely challenging as compared to the present demonstration with the square cylinder wake. To that end, we may be able to capitalize on the idea of autoencoder-based low dimensionalization [49], in addition to the present adaptive sampling. But we should caution that there may be a trade-off relationship between the compressibility and explainability of low-dimensionalized representation.…”

Section: Discussionmentioning

confidence: 99%

Supervised convolutional network for three-dimensional fluid data reconstruction from sectional flow fields with adaptive super-resolution assistance

Matsuo¹,

Nakamura²,

Morimoto³

et al. 2021

Preprint

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The recent development of high-performance computing enables us to generate spatiotemporal high-resolution data of nonlinear dynamical systems and to analyze them for deeper understanding of their complex nature. This trend can be found in a wide range of science and engineering communities, which suggests that detailed investigations on efficient data handling in physical science must be required in future. To this end, we introduce the use of convolutional neural networks (CNNs) to achieve an efficient data storage and estimation of scientific big data derived from nonlinear dynamical systems.The CNN is utilized to reconstruct three-dimensional data from a few numbers of two-dimensional sections in a computationally friendly manner. The present model is a combination of two-and three-dimensional CNNs, which allows users to save only some of the two-dimensional sections to reconstruct the volumetric data. As an example of threedimensional data, we consider a fluid flow around a square cylinder at the diameter-based Reynolds number Re D of 300, and show that volumetric fluid flow data can successfully be reconstructed with the present method from as few as five sections. Furthermore, we also propose a combination of the present CNN-based reconstruction with an adaptive sampling-based super-resolution analysis to augment the data compression capability of the present methods. Our report can be a significant bridge toward practical data handling for not only the fluid mechanics field but also a vast range of physical sciences.

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Section: Discussionmentioning

confidence: 99%

Supervised convolutional network for three-dimensional fluid data reconstruction from sectional flow fields with adaptive super-resolution assistance

Matsuo¹,

Nakamura²,

Morimoto³

et al. 2021

Preprint

Self Cite

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“…The filters, trainable parameters inside the CNN, are able to handle high-dimensional data efficiently and extract key features. Thanks to its unique capability in handling high-dimensional data, the use of CNN has also been spread in the fluid dynamics field in recent years [33,34,35,36,37,38,39,40,41,42].…”

Section: Convolutional Neural Networkmentioning

confidence: 99%

Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

Moriya,

Fukami,

Nabae

et al. 2021

Preprint

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We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved largeeddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall (∼ 10 wall units), while still resolving the near-wall region, to present a new path to save the computational cost. Convolutional neural network (CNN) is utilized to estimate a virtual wall-surface velocity from x − z sectional fields near the wall, whose training data are generated by a direct numerical simulation (DNS) at Re τ = 180. The virtual wall-surface velocity is prepared with the extrapolation of the DNS data near the wall. This idea enables us to give a proper wall condition to correct a velocity gradient near the wall. The estimation ability of the model from near wall information is first investigated as a priori test. The estimated velocity fields by the present CNN model are in statistical agreement with the reference DNS data. The model trained in a priori test is then combined with the LES as a posteriori test. We find that the LES can successfully be augmented using the present model at both the friction Reynolds number Re τ = 180 used for training and the unseen Reynolds number Re τ = 360 even when the first grid point is located at 5 wall units off the wall. We also investigate the robustness of the present model for the choice of sub-grid scale model and the possibility of transfer learning in a local domain. The observations through the paper suggest that the present model is a promising tool for recovering the accuracy of LES with a coarse grid near the wall.

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“…By renormalizing the initial graph to include self-loops (i.e. adding identity to the adjacency and degree matrices), they proposed the graph convolutional network (GCN) which obeys the propagation rule (5) x +1 = σ Px W , where x ∈ R |V|×n is a signal on the graph with n channels, W ∈ R n ×n +1 is a (potentially nonsquare) weight matrix containing the learnable parameters and…”

Section: A Graph Convolutional Autoencoder For Rommentioning

confidence: 99%

“…The work of Lee and Carlberg in [4] demonstrated that deep convolutional autoencoders (CAEs) can overcome the Kolmogorov width barrier for advection-dominated systems which limits linear ROM methods, leading to a variety of similar ROMs based on this architecture seen in e.g. [5,6,7,8]. Moreover, works such as [6,7] have experimented with entirely data-driven ROMs based on deep CAEs, and seen success using either fully connected or recurrent long short term networks to simulate the reduced low-dimensional dynamics.…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling

Gruber,

Gunzburger,

et al. 2021

Preprint

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The popularity of deep convolutional autoencoders (CAEs) has engendered effective reducedorder models (ROMs) for the simulation of large-scale dynamical systems. However, it is not known whether deep CAEs provide superior performance in all ROM scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large.

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Model order reduction with neural networks: Application to laminar and turbulent flows

Cited by 5 publications

References 67 publications

Supervised convolutional network for three-dimensional fluid data reconstruction from sectional flow fields with adaptive super-resolution assistance

Supervised convolutional network for three-dimensional fluid data reconstruction from sectional flow fields with adaptive super-resolution assistance

Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows

A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling

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