scholarly journals Challenges in dynamic mode decomposition

2021 ◽  
Vol 18 (185) ◽  
Author(s):  
Ziyou Wu ◽  
Steven L. Brunton ◽  
Shai Revzen
Keyword(s):  
Time Series ◽  
Numerical Models ◽  
Predictive Ability ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
System Matrix ◽  
Spatial And Temporal Patterns ◽  
Oscillatory Systems ◽  
Mode Decomposition ◽  
Wide Range

Dynamic mode decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics and neuroscience. Two of the main challenges remaining in DMD research are noise sensitivity and issues related to Krylov space closure when modelling nonlinear systems. Here, we investigate the combination of noise and nonlinearity in a controlled setting, by studying a class of systems with linear latent dynamics which are observed via multinomial observables. Our numerical models include system and measurement noise. We explore the influences of dataset metrics, the spectrum of the latent dynamics, the normality of the system matrix and the geometry of the dynamics. Our results show that even for these very mildly nonlinear conditions, DMD methods often fail to recover the spectrum and can have poor predictive ability. Our work is motivated by our experience modelling multilegged robot data, where we have encountered great difficulty in reconstructing time series for oscillatory systems with intermediate transients, which decay only slightly faster than a period.

scholarly journals Detecting regime transitions in time series using dynamic mode decomposition

2020 ◽  
Author(s):  
Georg Gottwald ◽  
Federica Gugole
Keyword(s):  
Time Series ◽  
Reconstruction Error ◽  
Reanalysis Data ◽  
Dynamic Mode Decomposition ◽  
Transient Dynamics ◽  
Dynamic Mode ◽  
Koopman Operator ◽  
Regime Changes ◽  
Fast Relaxation ◽  
Mode Decomposition

<p>We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically transient dynamics experiences the full state space dimension with subsequent fast relaxation towards the attractor. In equilibrium, on the other hand, the dynamics evolves on a slower time scale on a lower dimensional attractor. The reconstruction error of a dynamic mode decomposition is used to monitor the inability of the time series to resolve the fast relaxation towards the attractor as well as the effective dimension of the dynamics. We illustrate our method by detecting transient dynamics in the Kuramoto-Sivashinsky equation. We further apply our method to atmospheric reanalysis data; our diagnostics detects the transition from a predominantly negative North Atlantic Oscillation (NAO) to a predominantly positive NAO around 1970, as well as the recently found regime change in the Southern Hemisphere atmospheric circulation around 1970.</p>

scholarly journals Discovering Spatial-temporal Patterns of COVID-19 Pandemic in South Korea: A Data-driven Approach using Dynamic Mode Decomposition

2021 ◽  
Author(s):  
Sungchan Kim ◽  
Minseok Kim ◽  
Sunmi Lee ◽  
Young Ju Lee
Keyword(s):  
Time Series ◽  
South Korea ◽  
Time Series Data ◽  
Temporal Patterns ◽  
Dynamic Mode Decomposition ◽  
Series Data ◽  
Dynamic Mode ◽  
Regional Patterns ◽  
Effective Prevention ◽  
Mode Decomposition

Abstract A novel severe acute respiratory syndrome coronavirus 2 emerged in December 2019, and it took only a few months for WHO to declare COVID-19 as a pandemic in March 2020. It is very challenging to discover complex spatial-temporal transmission mechanisms. However, it is crucial to capture essential features of regional-temporal patterns of COVID-19 to implement prompt and effective prevention or mitigation interventions. In this work, we develop a novel framework of compatible window-wise dynamic mode decomposition (CwDMD) for nonlinear infectious disease dynamics. The compatible window is a selected representative subdomain of time series data, in which compatibility between spatial and temporal resolutions is established so that DMD can provide meaningful data analysis. A total of four compatible windows have been selected from COVID-19 time-series data from January 20, 2020, to May 10, 2021, in South Korea. The spatiotemporal patterns of these four windows are then analyzed. Several hot and cold spots were identified, their spatial-temporal relationships, and some hidden regional patterns were discovered. Our analysis reveals that the first wave was contained in Daegu and Gyeongbuk area but it spread rapidly to the whole of South Korea after the second wave. Later on, the spatial distribution is seen to become more homogeneous after the third wave. Our analysis also identifies that some patterns are not related to regional relevance. These findings have then been analyzed and associated with the inter-regional and local characteristics of South Korea. Thus, the present study is expected to provide public health officials helpful insights for future regional-temporal specific mitigation plans.

Advanced pattern techniques in weather and climate science

2021 ◽  
Author(s):  
Frank Kwasniok
Keyword(s):  
Large Scale ◽  
Traditional Approach ◽  
Climate Science ◽  
Dynamic Mode Decomposition ◽  
Low Rank ◽  
Dynamic Mode ◽  
State Variables ◽  
System Matrix ◽  
Mode Decomposition ◽  
Weather And Climate

<p>This presentation discusses two examples of the use of advanced pattern techniques in weather and climate science. Firstly, optimal mode decomposition (OMD) is employed for linear inverse modelling of large-scale atmospheric flow. The OMD technique determines a low-rank approximation to a high-dimensional dynamical system in terms of a linear empirical model; a set of patterns and a system matrix are identified simultaneously by maximising the explained predictive variance. The method is exemplified on a quasi-geostrophic atmospheric model with realistic mean state and variability. Considerable improvements in prediction skill are observed compared to the traditional approach based on principal components or dynamic mode decomposition (DMD). Secondly, nonlinear principal prediction patterns are used for stochastic subgrid-scale modelling. Pairs of predictor-predictand patterns are determined in the space of the resolved variables and the space of the subgrid forcing, respectively, and linked in a predictive manner. The predictor patterns may contain nonlinear functions of state variables. On top of this deterministic subgrid model the predictand patterns are forced stochastically. The approach is demonstrated on the two-scale Lorenz 1996 system.</p>

scholarly journals Parameter space and model reduction with shape parametrization, by means of active subspace and POD-Galerkin methods for industrial and biomedical applications

2018 ◽  
Author(s):  
Marco Tezzele ◽  
Francesco Ballarin ◽  
Andrea Mola ◽  
Gianluigi Rozza
Keyword(s):  
Model Reduction ◽  
Parameter Space ◽  
Biomedical Applications ◽  
Engineering Problem ◽  
Dynamic Mode Decomposition ◽  
Free Form ◽  
Dynamic Mode ◽  
Space Reduction ◽  
Mode Decomposition ◽  
Wide Range

In this work we present both industrial and biomedical applications, focusing on shape parametrization and parameter space reduction by means of active subspaces. In particular we introduce a combined parameter and model reduction methodology using a POD-Galerkin approach, and its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids [2]. The aim is to simulate a wide range of possible occlusions after the bifurcation of the carotid artery. A parametric description of the admissible deformations, based on radial basis functions interpolation technique implemented in the PyGeM python package, is introduced. The use of the reduced order model acting on the reduced parameter space allows significant computational savings and better performances. Moreover we present the reduction of heterogeneous parameter space in a naval engineering problem, that is the hydrodynamic flow past the hull of a ship advancing in calm water [3], considering structural and shape parameters. The geometrical parametrization is done via free form deformation. Some perspectives on a complete shape optimization pipeline by means of Dynamic Mode Decomposition (DMD) and POD with interpolation (PODI) are presented [1], together with the integration of the python packages PyDMD and EZyRB respectively.

scholarly journals Discovering spatiotemporal patterns of COVID-19 pandemic in South Korea

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sungchan Kim ◽  
Minseok Kim ◽  
Sunmi Lee ◽  
Young Ju Lee
Keyword(s):  
Time Series ◽  
South Korea ◽  
Time Series Data ◽  
Spatiotemporal Patterns ◽  
Dynamic Mode Decomposition ◽  
Series Data ◽  
Dynamic Mode ◽  
Regional Patterns ◽  
Effective Prevention ◽  
Mode Decomposition

AbstractA novel severe acute respiratory syndrome coronavirus 2 emerged in December 2019, and it took only a few months for WHO to declare COVID-19 as a pandemic in March 2020. It is very challenging to discover complex spatial–temporal transmission mechanisms. However, it is crucial to capture essential features of regional-temporal patterns of COVID-19 to implement prompt and effective prevention or mitigation interventions. In this work, we develop a novel framework of compatible window-wise dynamic mode decomposition (CwDMD) for nonlinear infectious disease dynamics. The compatible window is a selected representative subdomain of time series data, in which compatibility between spatial and temporal resolutions is established so that DMD can provide meaningful data analysis. A total of four compatible windows have been selected from COVID-19 time-series data from January 20, 2020, to May 10, 2021, in South Korea. The spatiotemporal patterns of these four windows are then analyzed. Several hot and cold spots were identified, their spatial–temporal relationships, and some hidden regional patterns were discovered. Our analysis reveals that the first wave was contained in the Daegu and Gyeongbuk areas, but it spread rapidly to the whole of South Korea after the second wave. Later on, the spatial distribution is seen to become more homogeneous after the third wave. Our analysis also identifies that some patterns are not related to regional relevance. These findings have then been analyzed and associated with the inter-regional and local characteristics of South Korea. Thus, the present study is expected to provide public health officials helpful insights for future regional-temporal specific mitigation plans.

Experimental Measurement of In-Plane Rolling Nonpneumatic Tire Vibrations Using High-Speed Imaging

2019 ◽  
Vol 47 (3) ◽  
pp. 196-210
Author(s):  
Meghashyam Panyam ◽  
Beshah Ayalew ◽  
Timothy Rhyne ◽  
Steve Cron ◽  
John Adcox
Keyword(s):  
High Speed ◽  
Image Correlation ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
High Speed Imaging ◽  
Correlation Algorithm ◽  
Mode Decomposition ◽  
Series Of Experiments ◽  
Plane Deformations ◽  
Dominant Frequencies

ABSTRACT This article presents a novel experimental technique for measuring in-plane deformations and vibration modes of a rotating nonpneumatic tire subjected to obstacle impacts. The tire was mounted on a modified quarter-car test rig, which was built around one of the drums of a 500-horse power chassis dynamometer at Clemson University's International Center for Automotive Research. A series of experiments were conducted using a high-speed camera to capture the event of the rotating tire coming into contact with a cleat attached to the surface of the drum. The resulting video was processed using a two-dimensional digital image correlation algorithm to obtain in-plane radial and tangential deformation fields of the tire. The dynamic mode decomposition algorithm was implemented on the deformation fields to extract the dominant frequencies that were excited in the tire upon contact with the cleat. It was observed that the deformations and the modal frequencies estimated using this method were within a reasonable range of expected values. In general, the results indicate that the method used in this study can be a useful tool in measuring in-plane deformations of rolling tires without the need for additional sensors and wiring.

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