A Reduced Order Deep Data Assimilation model

Casas, César Quilodrán; Arcucci, Rossella; Wu, Pin; Pain, Christopher C.; Guo, Yike

doi:10.1016/j.physd.2020.132615

Cited by 46 publications

(31 citation statements)

References 22 publications

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“…(2020b), Casas et al . (2020), and Bonavita and Laloyaux (2020). In practice, the trainable part of the surrogate model would be correcting the error of the knowledge‐based model: this is an offline model error estimation method.…”

Section: Introductionmentioning

confidence: 99%

Using machine learning to correct model error in data assimilation and forecast applications

Farchi

Laloyaux

Bonavita

et al. 2021

Quart J Royal Meteoro Soc

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The idea of using machine learning (ML) methods to reconstruct the dynamics of a system is the topic of recent studies in the geosciences, in which the key output is a surrogate model meant to emulate the dynamical model. In order to treat sparse and noisy observations in a rigorous way, ML can be combined with data assimilation (DA). This yields a class of iterative methods in which, at each iteration, a DA step assimilates the observations and alternates with a ML step to learn the underlying dynamics of the DA analysis. In this article, we propose to use this method to correct the error of an existing, knowledge-based model. In practice, the resulting surrogate model is a hybrid model between the original (knowledge-based) model and the ML model. We demonstrate the feasibility of the method numerically using a two-layer, two-dimensional, quasi-geostrophic channel model. Model error is introduced by the means of perturbed parameters. The DA step is performed using the strong-constraint 4D-Var algorithm, while the ML step is performed using deep learning tools. The ML models are able to learn a substantial part of the model error and the resulting hybrid surrogate models produce better short-to mid-range forecasts. Furthermore, using the hybrid surrogate models for DA yields a significantly better analysis than using the original model.

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Section: Introductionmentioning

confidence: 99%

Using machine learning to correct model error in data assimilation and forecast applications

Farchi

Laloyaux

Bonavita

et al. 2021

Quart J Royal Meteoro Soc

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“…18 modality blood flow data [73,74]. It is also possible to leverage neural networks for the optimization problem involved in combining ROM models from different datasets [75]. Modeling the effect of discrepancy in experimental and computational data by a feedback source term in the Navier-Stokes equations is a simple method that has been used in merging CFD and 4D flow MRI data [76].…”

Section: Discussionmentioning

confidence: 99%

Integrating multi-fidelity blood flow data with reduced-order data assimilation

Habibi¹,

D’Souza²,

Dawson³

et al. 2021

Preprint

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High-fidelity patient-specific modeling of cardiovascular flows and hemodynamics is challenging. Direct blood flow measurement inside the body with in-vivo measurement modalities such as 4D flow magnetic resonance imaging (4D flow MRI) suffer from low resolution and acquisition noise. In-vitro experimental modeling and patient-specific computational fluid dynamics (CFD) models are subject to uncertainty in patient-specific boundary conditions and model parameters. Furthermore, collecting blood flow data in the near-wall region (e.g., wall shear stress) with experimental measurement modalities poses additional challenges. In this study, a computationally efficient data assimilation method called reduced-order modeling Kalman filter (ROM-KF) was proposed, which combined a sequential Kalman filter with reduced-order modeling using a linear model provided by dynamic mode decomposition (DMD). The goal of ROM-KF was to overcome low resolution and noise in experimental and uncertainty in CFD modeling of cardiovascular flows. The accuracy of the method was assessed with 1D Womersley flow, 2D idealized aneurysm, and 3D patient-specific cerebral aneurysm models. Synthetic experimental data were used to enable direct quantification of errors using benchmark datasets. The accuracy of ROM-KF in reconstructing near-wall hemodynamics was assessed by applying the method to problems where near-wall blood flow data were missing in the experimental dataset. The ROM-KF method provided blood flow data that were more accurate than the computational and synthetic experimental datasets and improved near-wall hemodynamics quantification.

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“…The applications, often complex, related to multiphysics and nonlinear modeling with different model resolutions and prediction time horizons, vary from reservoir modeling (Kumar 2018 ), to geological feature prediction (Vo and Durlofsky 2014 ), to environmental modeling (Casas et al. 2020 ) and wildfire front-tracking problems (Rochoux et al. 2018 ).…”

Section: Introductionmentioning

confidence: 99%

A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping

et al. 2021

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An original graph clustering approach for the efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here, the localization term is very generic and refers to the idea of breaking up a global assimilation into subproblems. This unsupervised localization technique based on a linearized state-observation measure is general and does not rely on any prior information such as relevant spatial scales, empirical cutoff radii or homogeneity assumptions. Localization is performed via graph theory, a branch of mathematics emerging as a powerful approach to capturing complex and highly interconnected Earth and environmental systems in computational geosciences. The novel approach automatically segregates the state and observation variables in an optimal number of clusters, and it is more amenable to scalable data assimilation. The application of this method does not require underlying block-diagonal structures of prior covariance matrices. To address intercluster connectivity, two alternative data adaptations are proposed. Once the localization is completed, a covariance diagnosis and tuning are performed within each cluster, whose contribution is sequentially integrated into the entire covariance matrix. Numerical twin experiment tests show the reduced cost and added flexibility of this approach compared to global covariance tuning, and more accurate results yielded for both observation- and background-error parameter tuning.

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A Reduced Order Deep Data Assimilation model

Cited by 46 publications

References 22 publications

Using machine learning to correct model error in data assimilation and forecast applications

Using machine learning to correct model error in data assimilation and forecast applications

Integrating multi-fidelity blood flow data with reduced-order data assimilation

A Graph Clustering Approach to Localization for Adaptive Covariance Tuning in Data Assimilation Based on State-Observation Mapping

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