Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows

Pawar, Suraj; San, Omer

doi:10.1103/physrevfluids.6.050501

Cited by 32 publications

(9 citation statements)

References 116 publications

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“…As for surrogate networks coupled with DA algorithms, we have [42] and [11] which both consider Lorenz 96 system. In [42], Pawar and San model unresolved flow dynamics with a surrogate network and learn the correlation between resolved flow processes and unresolved subgrid variables thanks to a set of NNs. Whereas we both aim to more accurately forecast, their approach does not involve any space reduction technique.…”

Section: Related Work and Our Contributionsmentioning

confidence: 99%

“…A first ingredient in the approach we introduce in the present paper is to replace the (supposedly expensive) time integration of the model with a NN surrogate. Time stepping methods based on surrogates have already been explored by several authors [34,65,66,37,63,11,42].…”

Section: Related Work and Our Contributionsmentioning

confidence: 99%

“…The Lorenz 96 model [33] is widely used as a dynamical system [11,63,42] in ensemble data assimilation in particular for weather prediction.…”

Section: Etkf-q-latent Algorithmmentioning

confidence: 99%

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Latent Space Data Assimilation by using Deep Learning

Peyron,

Fillion,

Gürol

et al. 2021

Preprint

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Performing Data Assimilation (DA) at a low cost is of prime concern in Earth system modeling, particularly at the time of big data where huge quantities of observations are available. Capitalizing on the ability of Neural Networks techniques for approximating the solution of PDE's, we incorporate Deep Learning (DL) methods into a DA framework. More precisely, we exploit the latent structure provided by autoencoders (AEs) to design an Ensemble Transform Kalman Filter with model error (ETKF-Q) in the latent space. Model dynamics are also propagated within the latent space via a surrogate neural network. This novel ETKF-Q-Latent (thereafter referred to as ETKF-Q-L) algorithm is tested on a tailored instructional version of Lorenz 96 equations, named the augmented Lorenz 96 system: it possesses a latent structure that accurately represents the observed dynamics. Numerical experiments based on this particular system evidence that the ETKF-Q-L approach both reduces the computational cost and provides better accuracy than state of the art algorithms, such as the ETKF-Q.

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Section: Related Work and Our Contributionsmentioning

confidence: 99%

Section: Related Work and Our Contributionsmentioning

confidence: 99%

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Latent Space Data Assimilation by using Deep Learning

Peyron,

Fillion,

Gürol

et al. 2021

Preprint

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“…Deep learning (DL) has been applied to discovering new SGS models from the DNS data without any assumption of prior structural or functional form of the model [14][15][16][17][18][19][20]. The data-driven approach that employs convolutional neural network for learning the SGS model has also been used for different problems like two-dimensional decaying turbulence [11,21,22], three-dimensional decaying homogeneous isotropic turbulence [23], momentum forcing in ocean models [24], and subgrid-scale scalar flux modeling [25]. Moreover, neural networks have also been utilized to learn the optimal map between filtered and unfiltered variables in the approximate deconvolution framework for SGS modeling [26,27].…”

Section: Introductionmentioning

confidence: 99%

Frame invariant neural network closures for Kraichnan turbulence

Pawar,

San,

Rasheed

et al. 2022

Preprint

Self Cite

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Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we propose a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work builds a bridge between extensive physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

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“…Reduced-order models (ROMs) enhance the bridging between the physical and virtual world, providing real-time solutions [12]. The formulation and application of the ROMs can be found in various multi-query problems such as design optimization [19], data assimilation [20,21], and uncertainty quantification [22,23]. Reduced-order modeling is a mathematical approach, part of a broader category called surrogate modeling [7,24].…”

Section: Introductionmentioning

confidence: 99%

$\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

Drakoulas¹,

V.²,

Bourantas³

et al. 2022

Preprint

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Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the performance of complex systems. However, largescale, dynamic, non-linear models require significant computational resources and are prohibitive for real-time digital twin applications. To this end, reduced order models (ROMs) are employed, to approximate the high-fidelity solutions while accurately capturing the dominant aspects of the physical behavior. The present work proposes a new machine learning (ML) platform for the development of ROMs, to handle large-scale numerical problems dealing with transient nonlinear partial differential equations. Our framework, mentioned as FastSVD-ML-ROM, utilizes (i) a singular value decomposition (SVD) update methodology, to compute a linear subspace of the multi-fidelity solutions during the simulation process, (ii) convolutional autoencoders for nonlinear dimensionality reduction, (iii) feed-forward neural networks to map the input parameters to the latent spaces, and (iv) long short-term memory networks to predict and forecast the dynamics of parametric solutions. The efficiency of the FastSVD-ML-ROM framework is demonstrated for a 2D linear convection-diffusion equation, the problem of fluid around a cylinder, and the 3D blood flow inside an arterial segment. The accuracy of the reconstructed results demonstrates the robustness and assesses the efficiency of the proposed approach.

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Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows

Cited by 32 publications

References 116 publications

Latent Space Data Assimilation by using Deep Learning

Latent Space Data Assimilation by using Deep Learning

Frame invariant neural network closures for Kraichnan turbulence

$\textit{FastSVD-ML-ROM}$: A Reduced-Order Modeling Framework based on Machine Learning for Real-Time Applications

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