Modal Analysis of Turbulent Flow near an Inclined Bank–Longitudinal Structure Junction

Heydari, Nasser; Diplas, Panayiotis; Kutz, J. Nathan; Eshkevari, Soheil Sadeghi

doi:10.1061/(asce)hy.1943-7900.0001856

Cited by 8 publications

(7 citation statements)

References 30 publications

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“…It is further applied to a number of example spatio-temporal systems. It should be noted that alternative ways to improve DMD models include choosing appropriate windows of time for sampling data [15,35] and ensembling DMD regressions on short bursts of data, which was developed by Scandurra, Tezzele and Louiseau for the pyDMD package (Tutorial 8) [36]. These sampling strategies can also be used to great effect with the BOP-DMD algorithm, with the ensembling method being similar in spirit, but formalized and improved here with bagging and optimization.…”

Section: Introductionmentioning

confidence: 99%

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification

Sashidhar

Kutz

2022

Phil. Trans. R. Soc. A.

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Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A variety of regression techniques have been developed for producing the linear model approximation whose solutions are exponentials in time. For spatio-temporal data, DMD provides low-rank and interpretable models in the form of dominant modal structures along with their exponential/oscillatory behaviour in time. The majority of DMD algorithms, however, are prone to bias errors from noisy measurements of the dynamics, leading to poor model fits and unstable forecasting capabilities. The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities. Here, the optimized DMD algorithm is improved by using statistical bagging methods whereby a single set of snapshots is used to produce an ensemble of optimized DMD models. The outputs of these models are averaged to produce a bagging, optimized dynamic mode decomposition (BOP-DMD). BOP-DMD improves performance by stabilizing and cross-validating the DMD model by ensembling; it also robustifies the model and provides both spatial and temporal uncertainty quantification (UQ). Thus, unlike currently available DMD algorithms, BOP-DMD provides a stable and robust model for probabilistic , or Bayesian, forecasting with comprehensive UQ metrics. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

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Section: Introductionmentioning

confidence: 99%

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification

Sashidhar

Kutz

2022

Phil. Trans. R. Soc. A.

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“…Widely applied in physics ( Kac, 1966 ; Goldenfeld and Woese, 2011 ; Kantsler and Goldstein, 2012 ; Bhaduri et al, 2020 ), engineering ( Soong and Grigoriu, 1993 ; Heydari et al, 2021 ), and spectral computing ( Driscoll et al, 2014 ; Burns et al, 2020 ; Fortunato et al, 2021 ), mode representations ( Schmid, 2010 ; Tu et al, 2014 ) provide a powerful tool to decompose and study system dynamics at and across different energetic, spatial and temporal scales. In quantum systems, for example, mode representations in the form of carefully constructed eigenstates are used to characterize essential energetic system properties ( Slater and Koster, 1954 ; Jaynes and Cummings, 1963 ).…”

Section: Introductionmentioning

confidence: 99%

Learning developmental mode dynamics from single-cell trajectories

Romeo

Hastewell

Mietke

et al. 2021

eLife

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Embryogenesis is a multiscale process during which developmental symmetry breaking transitions give rise to complex multicellular organisms. Recent advances in high-resolution live-cell microscopy provide unprecedented insights into the collective cell dynamics at various stages of embryonic development. This rapid experimental progress poses the theoretical challenge of translating high-dimensional imaging data into predictive low-dimensional models that capture the essential ordering principles governing developmental cell migration in complex geometries. Here, we combine mode decomposition ideas that have proved successful in condensed matter physics and turbulence theory with recent advances in sparse dynamical systems inference to realize a computational framework for learning quantitative continuum models from single-cell imaging data. Considering pan-embryo cell migration during early gastrulation in zebrafish as a widely studied example, we show how cell trajectory data on a curved surface can be coarse-grained and compressed with suitable harmonic basis functions. The resulting low-dimensional representation of the collective cell dynamics enables a compact characterization of developmental symmetry breaking and the direct inference of an interpretable hydrodynamic model, which reveals similarities between pan-embryo cell migration and active Brownian particle dynamics on curved surfaces. Due to its generic conceptual foundation, we expect that mode-based model learning can help advance the quantitative biophysical understanding of a wide range of developmental structure formation processes.

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“…It is further applied to a number of example spatio-temporal systems. It should be noted that alternatives to improve DMD models include choosing appropriate windows of time for sampling data [13,32] and ensembling DMD regressions on short burst of data, which was developed by Scandurra, Tezzele and Louiseau for the pyDMD package (Tutorial 8) [33]. These sampling strategies can also be used to great effect with the BOP-DMD algorithm, with the ensembling method being similar in spirit, but formalized and improved here with bagging and optimization.…”

Section: Introductionmentioning

confidence: 99%

Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification

Sashidhar,

Kutz

2021

Preprint

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Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A diversity of regression techniques have been developed for producing the linear model approximation whose solutions are exponentials in time. For spatio-temporal data, DMD provides low-rank and interpretable models in the form of dominant modal structures along with their exponential/oscillatory behavior in time. The majority of DMD algorithms, however, are prone to bias errors from noisy measurements of the dynamics, leading to poor model fits and unstable forecasting capabilities. The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities. Here, the optimized DMD algorithm is improved by using statistical bagging methods whereby a single set of snapshots is used to produce an ensemble of optimized DMD models. The outputs of these models are averaged to produce a bagging, optimized dynamic mode decomposition (BOP-DMD). BOP-DMD not only improves performance, it also robustifies the model and provides both spatial and temporal uncertainty quantification (UQ). Thus unlike currently available DMD algorithms, BOP-DMD provides a stable and robust model for probabilistic, or Bayesian forecasting with comprehensive UQ metrics.

show abstract

Modal Analysis of Turbulent Flow near an Inclined Bank–Longitudinal Structure Junction

Cited by 8 publications

References 30 publications

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification

Learning developmental mode dynamics from single-cell trajectories

Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification

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