Modal Analysis of Fluid Flows: Applications and Outlook

Taira, Kunihiko; Hemati, Maziar S.; Brunton, Steven L.; Sun, Yiyang; Duraisamy, Karthik; Bagheri, Shervin; Dawson, Scott T. M.; Yeh, C.

doi:10.2514/1.j058462

Cited by 372 publications

(162 citation statements)

References 226 publications

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“…The field of supervised machine learning for fluid dynamics can be combined with other data-oriented architecture including linear-based methods [61,62], network science [63], and artificial intelligence. Prior to employing machine learning, users should care what type of fluid flow problems can really benefit from supervised machine learning with fluid dynamics.…”

Section: Discussionmentioning

confidence: 99%

Assessment of supervised machine learning methods for fluid flows

Fukami

Fukagata

Taira

2020

Theor. Comput. Fluid Dyn.

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162

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We apply supervised machine learning techniques to a number of regression problems in fluid dynamics. Four machine learning architectures are examined in terms of their characteristics, accuracy, computational cost, and robustness for canonical flow problems. We consider the estimation of force coefficients and wakes from a limited number of sensors on the surface for flows over a cylinder and NACA0012 airfoil with a Gurney flap. The influence of the temporal density of the training data is also examined. Furthermore, we consider the use of convolutional neural network in the context of super-resolution analysis of two-dimensional cylinder wake, two-dimensional decaying isotropic turbulence, and three-dimensional turbulent channel flow. In the concluding remarks, we summarize on findings from a range of regression type problems considered herein.

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Section: Discussionmentioning

confidence: 99%

Assessment of supervised machine learning methods for fluid flows

Fukami

Fukagata

Taira

2020

Theor. Comput. Fluid Dyn.

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162

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“…where Re is the dimensionless Reynolds number, defined as the ratio of inertial effects to viscous effects. Equation 15 can be rewritten as…”

Section: D Burgers Equationmentioning

confidence: 99%

A long short-term memory embedding for hybrid uplifted reduced order models

Ahmed

San

Rasheed

et al. 2020

Physica D: Nonlinear Phenomena

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In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n-width systems due to the underlying nonlinear processes. The third uplifting layer, called superresolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We performed numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.Keywords Hybrid analysis and modeling · Supervised machine learning · Long short-term memory · Model reduction · Galerkin projection · Grassmann manifold.Reduced order models (ROMs) have shown great success for prototypical problems in different fields. In particular, Galerkin projection (GP) coupled with proper orthogonal decomposition (POD) capability to extract the most energetic modes has been used to build ROMs for linear and nonlinear systems [22][23][24][25][26][27][28][29]. These ROMs preserve sufficient arXiv:1912.06756v1 [physics.flu-dyn]

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“…These reduced-order models (ROMs) find extensive application in control [5], multifidelity optimization [6], and uncertainty quantification [7,8], among others. We direct the interested reader to [9,10] for excellent reviews of the recent advances and opportunities in ROMs. To derive a ROM, one reduces the dimensionality of the full-order model (FOM), which comprises the PDEs in their discrete or semi-discrete form.…”

Section: Introductionmentioning

confidence: 99%

Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil

2020

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Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. Such models are known to incur huge off-line costs, however, which can sometimes outweigh their potential benefits. Furthermore, their prediction accuracy is known to be poor under transonic flow conditions. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks, and we demonstrate its ability to preserve accuracy with significantly lower offline and online costs. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in fast exploration of design space for diverse engineering applications. arXiv:1911.07943v2 [physics.flu-dyn] 12 Jan 2020 Ψ k (Au − f (u)) = 0.Since the reduced state variableũ ≈ Φ k u, this equation can be written as

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Modal Analysis of Fluid Flows: Applications and Outlook

Cited by 372 publications

References 226 publications

Assessment of supervised machine learning methods for fluid flows

Assessment of supervised machine learning methods for fluid flows

A long short-term memory embedding for hybrid uplifted reduced order models

Machine learning for nonintrusive model order reduction of the parametric inviscid transonic flow past an airfoil

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