A Dynamic Mode Decomposition Based Reduced-Order Model For Parameterized Time-Dependent Partial Differential Equations

Lin, Yifan; Gao, Zhen; Chen, Yuanhong; Sun, Xiaonan

doi:10.1007/s10915-023-02200-x

Cited by 2 publications

(1 citation statement)

References 51 publications

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“…For instance, Clainchey and et al proposed a higher order DMD (HODMD) method [24] that uses time-lagged snapshots and can be seen as superimposed DMD in a sliding window, which is also applied successfully to identify and extrapolate flow patterns [27]. Despite the DMD method is wildely used for reduced-order modelling of time-dependent problems, it is significantly more challenging for parameterized problems [28,29,30,31]. For solving this limitation, Syadi, Schmid and et al proposed a DMD-based parameter-dependent ROM framework for bifurcation analysis [32], where the time series HF solutions for different parameter values are "stacked" to form an augmented snapshot matrix, and the stacked DMD modes, which are calculated by the augmented snapshot matrix, are interpolated to form a new DMD mode for a new parameter.…”

Section: Introductionmentioning

confidence: 99%

Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function

et al. 2023

Journal of Computational Physics

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Section: Introductionmentioning

confidence: 99%

Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function

et al. 2023

Journal of Computational Physics

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Non-intrusive reduced-order model for time-dependent stochastic partial differential equations utilizing dynamic mode decomposition and polynomial chaos expansion

Wang,

Batool,

Sun

et al. 2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this study, we present a novel non-intrusive reduced-order model (ROM) for solving time-dependent stochastic partial differential equations (SPDEs). Utilizing proper orthogonal decomposition (POD), we extract spatial modes from high-fidelity solutions. A dynamic mode decomposition (DMD) method is then applied to vertically stacked matrices of projection coefficients for future prediction of coefficient fields. Polynomial chaos expansion (PCE) is employed to construct a mapping from random parameter inputs to the DMD-predicted coefficient field. These lead to the POD–DMD–PCE method. The innovation lies in vertically stacking projection coefficients, ensuring time-dimensional consistency in the coefficient matrix for DMD and facilitating parameter integration for PCE analysis. This method combines the model reduction of POD with the time extrapolation strengths of DMD, effectively recovering field solutions both within and beyond the training time interval. The efficiency and time extrapolation capabilities of the proposed method are validated through various nonlinear SPDEs. These include a reaction–diffusion equation with 19 parameters, a two-dimensional heat equation with two parameters, and a one-dimensional Burgers equation with three parameters.

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A Dynamic Mode Decomposition Based Reduced-Order Model For Parameterized Time-Dependent Partial Differential Equations

Cited by 2 publications

References 51 publications

Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function

Surrogate modeling of time-domain electromagnetic wave propagation via dynamic mode decomposition and radial basis function

Non-intrusive reduced-order model for time-dependent stochastic partial differential equations utilizing dynamic mode decomposition and polynomial chaos expansion

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