Continuous data assimilation reduced order models of fluid flow

Zerfas, Camille; Rebholz, Leo G.; Schneier, Michael; Iliescu, Traian

doi:10.1016/j.cma.2019.112596

Cited by 50 publications

(29 citation statements)

References 42 publications

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“…The main advantage of this non-intrusive approach is that it does not require the information about the equations governing the full order model. Although the proposed approach helps to generate a NIROM framework solely from the snapshot data reconstructed onto a POD-spanned space, it may still suffer from fundamental challenges of traditional POD-Galerkin models (e.g., we refer to Zerfas et al 120 for a recent discussion about ways to mitigate their lack of accuracy).…”

Section: Introductionmentioning

confidence: 99%

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

et al. 2019

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In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equations, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a non-intrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly non-intrusive, since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate, and can be used as a robust predictive tool for non-intrusive model order reduction of complex fluid flows.

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Section: Introductionmentioning

confidence: 99%

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

et al. 2019

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“…13 Recent works have also drawn ideas to synthesize DA with reduced order models. [14][15][16][17][18][19][20][21][22][23] Bocquet et al 24 proposed a hybrid framework by combining DA and machine learning (ML) to estimate the model, the state trajectory, and model error statistics for high-dimensional chaotic systems from partial and noisy observations. Brajard et al 25 proposed an algorithm where neural networks provide a surrogate forward model to DA, and DA provides a time series of complete states to train the neural network.…”

Section: Introductionmentioning

confidence: 99%

Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

et al. 2020

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Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor-corrector type nudging approaches are still attractive due to their simplicity of implementation when more complex methods need to be avoided. However, optimal estimate of the nudging gain matrix might be cumbersome. In this paper, we put forth a fully nonintrusive recurrent neural network approach based on a long shortterm memory (LSTM) embedding architecture to estimate the nudging term, which plays a role not only to force the state trajectories to the observations but also acts as a stabilizer. Furthermore, our approach relies on the power of archival data, and the trained model can be retrained effectively due to the power of transfer learning in any neural network applications. In order to verify the feasibility of the proposed approach, we perform twin experiments using the Lorenz 96 system. Our results demonstrate that the proposed LSTM nudging approach yields more accurate estimates than both the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) when only sparse observations are available. With the availability of emerging artificial intelligence friendly and modular hardware technologies and heterogeneous computing platforms, we articulate that our simplistic nudging framework turns out to be computationally more efficient than either the EKF or EnKF approaches.

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“…Other than meteorology [29], DA tools are gaining popularity in different disciplines like reservoir engineering [30] and neuroscience [31]. Recent works have also drawn techniques and ideas from DA to enrich reduced order modeling of fluid flows and vice versa [32][33][34][35][36][37][38][39][40]. In conventional projection-based model reduction approaches, a set of system's realizations are used to build a reduced order model (ROM) that sufficiently represent the system's dynamics with significantly lower computational cost [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, a 4D-VAR approach has been suggested to provide an optimal nonlinear eddy viscosity estimate in Galerkin projection based ROMs [32]. An adaptive nudging technique has also been recently introduced to force ROMs toward the reference solution corresponding to the observed data [33].…”

Section: Introductionmentioning

confidence: 99%

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction

et al. 2020

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In this paper, we propose a variational approach to estimate eddy viscosity using forward sensitivity method (FSM) for closure modeling in nonlinear reduced order models. FSM is a data assimilation technique that blends model's predictions with noisy observations to correct initial state and/or model parameters. We apply this approach on a projection based reduced order model (ROM) of the one-dimensional viscous Burgers equation with a square wave defining a moving shock, and the two-dimensional vorticity transport equation formulating a decay of Kraichnan turbulence. We investigate the capability of the approach to approximate an optimal value for eddy viscosity with different measurement configurations. Specifically, we show that our approach can sufficiently assimilate information either through full-field or sparse noisy measurements to estimate eddy viscosity closure to cure standard Galerkin reduced order model (GROM) predictions. Therefore, our approach provides a modular framework to correct forecasting error from a sparse observational network on a latent space. We highlight that the proposed GROM-FSM framework is promising for emerging digital twin applications, where real-time sensor measurements can be used to update and optimize surrogate model's parameters.

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Continuous data assimilation reduced order models of fluid flow

Cited by 50 publications

References 42 publications

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

Long short-term memory embedded nudging schemes for nonlinear data assimilation of geophysical flows

Forward sensitivity approach for estimating eddy viscosity closures in nonlinear model reduction

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