Robust flow reconstruction from limited measurements via sparse representation

Callaham, Jared; Maeda, Kazuki; Brunton, Steven L.

doi:10.1103/physrevfluids.4.103907

Cited by 129 publications

(64 citation statements)

References 120 publications

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“…This scheme has already been tested in twodimensional barotropic flows [21] and weather models [22], showing better results than linear DA schemes, but still presenting nontrivial obstacles when scaling to highdimensional systems. New techniques based on machine learning have been applied to the flow reconstruction problem as well [23,24], but only on two-dimensional flows. One important point to make about the aforementioned techniques is that they can be hard and/or very expensive to scale to three-dimensional flows.…”

Section: Introductionmentioning

confidence: 99%

Synchronization to Big Data: Nudging the Navier-Stokes Equations for Data Assimilation of Turbulent Flows

Leoni

Mazzino²,

Biferale

2020

Phys. Rev. X

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Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it to the canonical problem of fluid dynamics: three-dimensional homogeneous and isotropic turbulence. By doing numerical experiments we perform a systematic assessment of how well the technique reconstructs large-and small-scale features of the flow with respect to the quantity and the quality or type of data supplied to it. The types of data used are (i) field values on a fixed number of spatial locations (Eulerian nudging), (ii) Fourier coefficients of the fields on a fixed range of wave numbers (Fourier nudging), or (iii) field values along a set of moving probes inside the flow (Lagrangian nudging). We present state-of-the-art quantitative measurements of the scale-by-scale transition to synchronization and a detailed discussion of the probability distribution function of the reconstruction error, by comparing the nudged field and the truth point by point. Furthermore, we show that for more complex flow configurations, like the case of anisotropic rotating turbulence, the presence of cyclonic and anticyclonic structures leads to unexpectedly better performances of the algorithm. We discuss potential further applications of nudging to a series of applied flow configurations, including the problem of field reconstruction in thermal Rayleigh-Bénard convection and in magnetohydrodynamics, and to the determination of optimal parametrization for small-scale turbulent modeling. Our study fixes the standard requirements for future applications of nudging to complex turbulent flows.

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Section: Introductionmentioning

confidence: 99%

Synchronization to Big Data: Nudging the Navier-Stokes Equations for Data Assimilation of Turbulent Flows

Leoni

Mazzino²,

Biferale

2020

Phys. Rev. X

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“…The first method used is the most common implementation of sparse recovery originating from the compressed sensing literature (Donoho, 2006;Candès and Wakin, 2008;Callaham et al, 2019). This method allows to calculate a set of coefficients that approximate the real coefficients by taking advantage of the fact that many entries of the global basis are negligibly small (c.f.…”

Section: Methods 1: Sparse Recovery Reconstructionmentioning

confidence: 99%

“…Sparse reconstruction is a technique used to obtain accurate details about the full scale features of a system using a sparse subset of information (e.g., a few pixels or measurements within the system) and has been the subject of interest for some decades (Candès, 2006;Donoho, 2006). Applications for such state estimation problems range from reconstructing faces from limited or corrupted data (Wright et al, 2008) to deblurring and improving image resolution (Dong et al, 2011) to estimating global sea surface temperatures (Manohar et al, 2018;Callaham et al, 2019). The literature concerning state estimation and sparse reconstruction is rapidly developing.…”

Section: Introductionmentioning

confidence: 99%

Data-driven sparse reconstruction of flow over a stalled aerofoil using experimental data

Carter

Voogt

Soares

et al. 2021

DCE

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Recent work has demonstrated the use of sparse sensors in combination with the proper orthogonal decomposition (POD) to produce data-driven reconstructions of the full velocity fields in a variety of flows. The present work investigates the fidelity of such techniques applied to a stalled NACA 0012 aerofoil at $ {Re}_c=75,000 $ at an angle of attack $ \alpha ={12}^{\circ } $ as measured experimentally using planar time-resolved particle image velocimetry. In contrast to many previous studies, the flow is absent of any dominant shedding frequency and exhibits a broad range of singular values due to the turbulence in the separated region. Several reconstruction methodologies for linear state estimation based on classical compressed sensing and extended POD methodologies are presented as well as nonlinear refinement through the use of a shallow neural network (SNN). It is found that the linear reconstructions inspired by the extended POD are inferior to the compressed sensing approach provided that the sparse sensors avoid regions of the flow with small variance across the global POD basis. Regardless of the linear method used, the nonlinear SNN gives strikingly similar performance in its refinement of the reconstructions. The capability of sparse sensors to reconstruct separated turbulent flow measurements is further discussed and directions for future work suggested.

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“…Our final number of snapshots for training amounts to 427, and for testing amounts to 1487. This train–test split of the dataset is a common configuration for data-driven studies [40] and the 8 year training period captures several short- and long-term trends in the global sea-surface temperature. Individual training samples are constructed by selecting a window of inputs (from the past) and a corresponding window of outputs (for the forecast task in the future) from the set of 427 training snapshots.…”

Section: Dataset(s)mentioning

confidence: 99%

Simple, low-cost and accurate data-driven geophysical forecasting with learned kernels

2021

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Modelling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned from data (using kernel flows, a variant of cross-validation), then the resulting data-driven models are not only faster than equation-based models but are easier to train than neural networks such as the long short-term memory neural network. In addition, they are also more accurate and predictive than the latter. When trained on geophysical observational data, for example the weekly averaged global sea-surface temperature, considerable gains are also observed by the proposed technique in comparison with classical partial differential equation-based models in terms of forecast computational cost and accuracy. When trained on publicly available re-analysis data for the daily temperature of the North American continent, we see significant improvements over classical baselines such as climatology and persistence-based forecast techniques. Although our experiments concern specific examples, the proposed approach is general, and our results support the viability of kernel methods (with learned kernels) for interpretable and computationally efficient geophysical forecasting for a large diversity of processes.

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Robust flow reconstruction from limited measurements via sparse representation

Cited by 129 publications

References 120 publications

Synchronization to Big Data: Nudging the Navier-Stokes Equations for Data Assimilation of Turbulent Flows

Synchronization to Big Data: Nudging the Navier-Stokes Equations for Data Assimilation of Turbulent Flows

Data-driven sparse reconstruction of flow over a stalled aerofoil using experimental data

Simple, low-cost and accurate data-driven geophysical forecasting with learned kernels

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