Randomized Algorithms for Non-Intrusive Parametric Reduced Order Modeling

Rajaram, Dushhyanth; Perron, Christian; Puranik, Tejas G.; Mavris, Dimitri N.

doi:10.2514/1.j059616

Cited by 17 publications

(6 citation statements)

References 25 publications

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“…where F 1 and G 1 capture the range and corange of X 1 , respectively, while H 1 is called the core sketch and describes how X 1 acts between the spaces captured by sketches F 1 and G 1 [54]. Now, near-optimal bases for the range and corange of X 1 are computed by the thin QR factorization of F 1 and G 1 as follows:…”

Section: B Sketching the Range Of Xmentioning

confidence: 99%

Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations

Ahmed,

San,

Bistrian

et al. 2022

Preprint

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Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical roots from the Koopman approximation theory. Indeed, DMD may be viewed as the data-driven realization of the famous Koopman operator. Nonetheless, the stable implementation of DMD incurs computing the singular value decomposition of the input data matrix. This, in turn, makes the process computationally demanding for high dimensional systems. In order to alleviate this burden, we develop a framework based on sketching methods, wherein a sketch of a matrix is simply another matrix which is significantly smaller, but still sufficiently approximates the original system. Such sketching or embedding is performed by applying random transformations, with certain properties, on the input matrix to yield a compressed version of the initial system. Hence, many of the expensive computations can be carried out on the smaller matrix, thereby accelerating the solution of the original problem. We conduct numerical experiments conducted using the spherical shallow water equations as a prototypical model in the context of geophysical flows. The performance of several sketching approaches is evaluated for capturing the range and co-range of the data matrix. The proposed sketching-based framework can accelerate various portions of the DMD algorithm, compared to classical methods that operate directly on the raw input data. This eventually leads to substantial computational gains that are vital for digital twinning of high dimensional systems.

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Section: B Sketching the Range Of Xmentioning

confidence: 99%

Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations

Ahmed,

San,

Bistrian

et al. 2022

Preprint

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“…The use of ROMs in aerospace applications has been primarily in advanced Computational Fluid Dynamics applications such as those involving unsteady aerodynamics, aero-elastic effects, hypersonic flow fields etc. [21][22][23][24][25]. These models have also been used for multi-disciplinary design, analysis, and optimization applications such as the design optimization of airfoils [26].…”

Section: Reduced Order Modelingmentioning

confidence: 99%

Reduced Order Modeling Methods for Aviation Noise Estimation

et al. 2021

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A key enabler for sustainable growth of aviation is the mitigation of adverse environmental effects. One area of concern is community noise exposure at large hub airports serving growing population centers. Traditionally, community noise exposure is computed using noise contours around airports, which requires knowledge of a large dataset pertaining to the air traffic operations at the airport of interest. Due to the underlying variability in real-world aircraft operations, numerous assumptions need to be made which adversely affect the accuracy of the model. Reduced-Order Modeling (ROM) methods provide a new framework for the retention of a large number of these parameters, thus improving model speed and accuracy. In this work, a proper orthogonal decomposition in conjunction with a response surface methodology-based surrogate model is used to create a rapid noise assessment model. Validation is performed against results obtained from the aviation environmental design tool with quantitative error metrics and visual contour comparisons. Obtained results are encouraging and motivate further work in this area with other ROM methods. ROM based models for noise assessment expand the solution space for noise mitigation strategies which can be evaluated, and therefore can lead to novel solutions which cannot be found with traditional modeling methods.

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“…Firstly, the snapshot matrix becomes very large for problems with many time steps and parameter samples, leading to expensive singular-value decomposition (SVD). For this issue, methods such as the randomized SVD algorithm [31], fast adaptive cross-approximation [32], and local bases solutions method [33] have been used for large-scale problems. Beyond this, Wang et al [34] applied POD twice to reduce the cost of global spatial bases for unsteady flow problems in the parameter domain.…”

Section: Introductionmentioning

confidence: 99%

Non-Intrusive Reduced-Order Modeling Based on Parametrized Proper Orthogonal Decomposition

Li,

Pan,

Zhou

et al. 2023

Energies

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A new non-intrusive reduced-order modeling method based on space-time parameter decoupling for parametrized time-dependent problems is proposed. This method requires the preparation of a database comprising high-fidelity solutions. The spatial bases are extracted from the database through first-level proper orthogonal decomposition (POD). The algebraic relationship between the time trajectory/parameter positions and the projection coefficient is described by the linear superposition of the second-level POD bases (temporal bases) and the second-level projection coefficients (parameter-dependent coefficients). This decomposition strategy decouples the space-time parameter effects, providing a stable foundation for fast predictions of parametrized time-dependent problems. The mappings between the parameter locations and the parameter-dependent coefficients are approximated as Gaussian process regression (GPR) models. The accuracy and efficiency of the PPOD-ROM are demonstrated through two numerical examples: flows past a cylinder and turbine flows with a clocking effect.

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Randomized Algorithms for Non-Intrusive Parametric Reduced Order Modeling

Cited by 17 publications

References 25 publications

Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations

Sketching Methods for Dynamic Mode Decomposition in Spherical Shallow Water Equations

Reduced Order Modeling Methods for Aviation Noise Estimation

Non-Intrusive Reduced-Order Modeling Based on Parametrized Proper Orthogonal Decomposition

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