A novel framework for cost-effectively reconstructing the global flow field by super-resolution

Wang, Longyan; Luo, Zhaohui; Xu, Jianzhong; Luo, Wei; Yuan, Jianping

doi:10.1063/5.0062775

Cited by 15 publications

(5 citation statements)

References 22 publications

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“…Figure 3 outlines the network architecture, which is based on U‐Net (Ronneberger et al., 2015). U‐Net architectures have been employed in the SR for fluid systems (e.g., Hammoud et al., 2022; Jiang et al., 2020; L. Wang et al., 2021). The input and output of the NN are vorticity fields.…”

Section: Methodsmentioning

confidence: 99%

Spatio‐Temporal Super‐Resolution Data Assimilation (SRDA) Utilizing Deep Neural Networks With Domain Generalization

Yasuda,

Onishi

2023

J Adv Model Earth Syst

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Deep learning has recently gained attention in the atmospheric and oceanic sciences for its potential to improve the accuracy of numerical simulations or to reduce computational costs. Super‐resolution is one such technique for high‐resolution inference from low‐resolution data. This paper proposes a new scheme, called four‐dimensional super‐resolution data assimilation (4D‐SRDA). This framework calculates the time evolution of a system from low‐resolution simulations using a physics‐based model, while a trained neural network simultaneously performs data assimilation and spatio‐temporal super‐resolution. The use of low‐resolution simulations without ensemble members reduces the computational cost of obtaining inferences at high spatio‐temporal resolution. In 4D‐SRDA, physics‐based simulations and neural‐network inferences are performed alternately, possibly causing a domain shift, that is, a statistical difference between the training and test data, especially in offline training. Domain shifts can reduce the accuracy of inference. To mitigate this risk, we developed super‐resolution mixup (SR‐mixup)–a data augmentation method for domain generalization. SR‐mixup creates a linear combination of randomly sampled inputs, resulting in synthetic data with a different distribution from the original data. The proposed methods were validated using an idealized barotropic ocean jet with supervised learning. The results suggest that the combination of 4D‐SRDA and SR‐mixup is effective for robust inference cycles. This study highlights the potential of super‐resolution and domain‐generalization techniques, in the field of data assimilation, especially for the integration of physics‐based and data‐driven models.

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Section: Methodsmentioning

confidence: 99%

Spatio‐Temporal Super‐Resolution Data Assimilation (SRDA) Utilizing Deep Neural Networks With Domain Generalization

Yasuda,

Onishi

2023

J Adv Model Earth Syst

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“…In the subsequent studies, the DSC/MS was applied to the three-dimensional velocity 27,28 ; the spatio-temporal super-resolution was performed by the successive use of DSC/MS in space and time; 28 a deeper version of DSC/MS was proposed. 29 Although the DSC/MS was proposed relatively early, it is still one of the most important CNNs in the fluid super-resolution.…”

Section: B Methods Of Making Equivariant Cnnsmentioning

confidence: 99%

“…CNNs have succeeded in super-resolving two-dimensional fluids [23][24][25][26][27][28][29] and large-scale flows in the ocean and atmosphere. 40,42,43,45,46 These results suggest that the long-range interacting nature is not critical to the superresolution in practice, and the gauge equivariant CNNs 78,79 may be useful for the fluid super-resolution.…”

Section: Equivariance To Local Rotationmentioning

confidence: 99%

“…Super-resolution is studied in computer vision as an application of NNs. [18][19][20][21][22] The success of these NNs has led to an increasing number of studies on the fluid-related SR: idealized turbulent flows in two [23][24][25][26][27][28][29] and three dimensions, 27,28,[30][31][32] Rayleigh-Bénard convection, 33 smoke motions in turbulent flows, [34][35][36] flows in blood vessels, [37][38][39] sea surface temperature, 25,40 and atmospheric fields. [41][42][43][44][45][46][47][48] Physics laws such as the continuity equation can be taken into account as the prior knowledge, which makes super-resolved flows more accurate and physically valid.…”

Section: Introductionmentioning

confidence: 99%

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Roto-Translation Equivariant Super-Resolution of Two-Dimensional Flows Using Convolutional Neural Networks

Yasuda¹,

Onishi²

2022

Preprint

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Convolutional neural networks (CNNs) often process vectors as quantities having no direction like colors in images. This study investigates the effect of treating vectors as geometrical objects in terms of super-resolution of velocity on two-dimensional fluids. Vector is distinguished from scalar by the transformation law associated with a change in basis, which can be incorporated as the prior knowledge using the equivariant deep learning. We convert existing CNNs into equivariant ones by making each layer equivariant with respect to rotation and translation. The training data in the low-and high-resolution are generated with the downsampling or the spectral nudging. When the data inherit the rotational symmetry, the equivariant CNNs show comparable accuracy with the non-equivariant ones. Since the number of parameters is smaller in the equivariant CNNs, these models are trainable with a smaller size of the data. In this case, the transformation law of vector should be incorporated as the prior knowledge, where vector is explicitly treated as a quantity having direction. Two examples demonstrate that the symmetry of the data can be broken. In the first case, a downsampling method makes the correspondence between low-and high-resolution patterns dependent on the orientation. In the second case, the input data are insufficient to recognize the rotation of coordinates in the experiment with the spectral nudging. In both cases, the accuracy of the CNNs deteriorates if the equivariance is forced to be imposed, and the usage of conventional CNNs may be justified even though vector is processed as a quantity having no direction.

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“…PINN, on the other hand, uses the residuals of the physical governing equations to form a loss function for neural network training, which serves as a penalty to restrict the space of feasible solutions. PINN can also combine traditional physical models with sparse high-fidelity measurements to reconstruct flow fields (Karpatne et al , 2017; Eivazi and Vinuesa, 2022), which has been a research hotspot and attracted tremendous attention in recent years (Wang et al , 2021; Wang et al , 2022). For instance, Arzani et al (2021) applied the PINN strategy to near-wall blood flow reconstruction, which incorporated the fluid governing functions and sparse internal data into the loss function.…”

Section: Introductionmentioning

confidence: 99%

Time-averaged flow field reconstruction based on a multifidelity model using physics-informed neural network (PINN) and nonlinear information fusion

Rui,

Zeng,

et al. 2023

HFF

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Purpose Current methods for flow field reconstruction mainly rely on data-driven algorithms which require an immense amount of experimental or field-measured data. Physics-informed neural network (PINN), which was proposed to encode physical laws into neural networks, is a less data-demanding approach for flow field reconstruction. However, when the fluid physics is complex, it is tricky to obtain accurate solutions under the PINN framework. This study aims to propose a physics-based data-driven approach for time-averaged flow field reconstruction which can overcome the hurdles of the above methods. Design/methodology/approach A multifidelity strategy leveraging PINN and a nonlinear information fusion (NIF) algorithm is proposed. Plentiful low-fidelity data are generated from the predictions of a PINN which is constructed purely using Reynold-averaged Navier–Stokes equations, while sparse high-fidelity data are obtained by field or experimental measurements. The NIF algorithm is performed to elicit a multifidelity model, which blends the nonlinear cross-correlation information between low- and high-fidelity data. Findings Two experimental cases are used to verify the capability and efficacy of the proposed strategy through comparison with other widely used strategies. It is revealed that the missing flow information within the whole computational domain can be favorably recovered by the proposed multifidelity strategy with use of sparse measurement/experimental data. The elicited multifidelity model inherits the underlying physics inherent in low-fidelity PINN predictions and rectifies the low-fidelity predictions over the whole computational domain. The proposed strategy is much superior to other contrastive strategies in terms of the accuracy of reconstruction. Originality/value In this study, a physics-informed data-driven strategy for time-averaged flow field reconstruction is proposed which extends the applicability of the PINN framework. In addition, embedding physical laws when training the multifidelity model leads to less data demand for model development compared to purely data-driven methods for flow field reconstruction.

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A novel framework for cost-effectively reconstructing the global flow field by super-resolution

Cited by 15 publications

References 22 publications

Spatio‐Temporal Super‐Resolution Data Assimilation (SRDA) Utilizing Deep Neural Networks With Domain Generalization

Spatio‐Temporal Super‐Resolution Data Assimilation (SRDA) Utilizing Deep Neural Networks With Domain Generalization

Roto-Translation Equivariant Super-Resolution of Two-Dimensional Flows Using Convolutional Neural Networks

Time-averaged flow field reconstruction based on a multifidelity model using physics-informed neural network (PINN) and nonlinear information fusion

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