A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

Rahman, Sk. Mashfiqur; San, Omer; Rasheed, Adil

doi:10.3390/fluids3040086

Cited by 32 publications

(25 citation statements)

References 88 publications

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“…The BVE model shares many features with the twodimensional Euler and Navier-Stokes equations and has been extensively used over the years to describe various aspects of the largest scales of turbulent geophysical fluid dynamics [80][81][82][83][84][85]. Using β−plane assumption reasonable for most oceanic flows, the dimensionless vorticitystreamfunction formulation of the forced-dissipative BVE can be written as [52]:…”

Section: Single-layer Quasi-geostrophic (Qg) Ocean Circulation Modelmentioning

confidence: 99%

“…Hence, in our study, we utilize numerical schemes suited for simulation of such type of ocean models and for long-time integration. Details of the relevant numerical discretization schemes, Poisson solver, and problem definitions for this study can be found in elsewhere [52,78,88].…”

Section: Single-layer Quasi-geostrophic (Qg) Ocean Circulation Modelmentioning

confidence: 99%

“…With the growing interest in data-driven modeling of ROMs using machine learning (ML) architectures, there has been another dimension of research introduced to the community for the improvement in ROM performance, referred as hybrid ROM approach. Generally, the hybridization is done by combining an imperfect physics-based model with a data-driven technique to get a hybrid scheme, and it is observed that the hybrid model shows better predictive performance than the component models [52][53][54][55].…”

Section: Introductionmentioning

confidence: 99%

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Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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In this study, we present a non-intrusive reduced order modeling (ROM) framework for largescale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the highresolution data snapshots using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully non-intrusive ROM framework is robust and capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.

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Section: Single-layer Quasi-geostrophic (Qg) Ocean Circulation Modelmentioning

confidence: 99%

Section: Single-layer Quasi-geostrophic (Qg) Ocean Circulation Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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“…The above correction term can be learned with datadriven machine learning algorithm [28,43]. We employ long-short term memory architecture [44], a variant of recurrent neural network to learn this correction.…”

Section: Evolve-then-correct Approachmentioning

confidence: 99%

An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

et al. 2020

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In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then formulate a recurrent neural network emulator based on the assumption that observed data is a manifestation of all relevant processes. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-thencorrect approach toward realtime simulations, where the full process model is not known a priori.

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“…Until recently, the fully non-intrusive modeling can be considered most attractive enabling methodology to do real-time simulation very efficiently in the context of emerging digital twin technologies [103]. In a complimentary fashion, the hybrid models [104][105][106][107][108][109] are developed by combining the intrusive and non-intrusive models in such way that the limitation of one component modeling strategy can be addressed by the other component model.…”

Section: Introductionmentioning

confidence: 99%

Memory embedded non-intrusive reduced order modeling of non-ergodic flows

et al. 2019

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Generating a digital twin of any complex system requires modeling and computational approaches that are efficient, accurate, and modular. Traditional reduced order modeling techniques are targeted at only the first two but the novel non-intrusive approach presented in this study is an attempt at taking all three into account effectively compared to their traditional counterparts. Based on dimensionality reduction using proper orthogonal decomposition (POD), we introduce a long short-term memory (LSTM) neural network architecture together with a principal interval decomposition (PID) framework as an enabler to account for localized modal deformation, which is a key element in accurate reduced order modeling of convective flows. Our applications for convection dominated systems governed by Burgers, Navier-Stokes, and Boussinesq equations demonstrate that the proposed approach yields significantly more accurate predictions than the POD-Galerkin method, and could be a key enabler towards near real-time predictions of unsteady flows. and perhaps much beyond. With the recent wave of digitization, reduced order modeling can be viewed as one of the key enablers to bring the promise of the digital twinning concept closer to reality [38]. Therefore, there is a continuous demand for the development of accurate reduced order models for complex physical phenomena. In projection-based ROMs, the most widely used technique, the discrete high-dimensional operators are projected onto a lower-dimensional space, so that the problem can be solved more efficiently in this reduced space [39][40][41][42][43][44].One of the very early-developed and well-known approaches to build this reduced space is Fourier analysis. However, it assumes universal basis functions (or modes) which have no specific relation to the physical system. On the other hand, snapshot-based model reduction techniques tailor a reduced space that best fits the problem by extracting the underlying coherent structures that controls the major dynamical evolution we are interested in. Proper orthogonal decomposition (POD) is a very popular and well-established approach extracting the modes which most contributes to the total variance [45,46]. In fluid dynamics applications, where we are mostly interested in the velocity field, those modes contain the largest amount of kinetic energy [47,48]. That is why POD is usually classified as an energy-based decomposition method. Another popular approach for model order reduction is the dynamic mode decomposition (DMD) [49][50][51][52][53][54] which generates a number of modes, each characterized by an oscillating frequency and growth/decay rate. In the present study, we are interested in the application of POD for dimensionality reduction.POD generates a set of spatial orthonormal basis functions, each containing a significant amount of total energy. To obtain a reduced representation of a system, the first few modes are selected, and the remaining are truncated assuming their contribution to the system's behavior is minimum (i.e.,...

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A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence

Cited by 32 publications

References 88 publications

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

Memory embedded non-intrusive reduced order modeling of non-ergodic flows

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