On reduced input-output dynamic mode decomposition

Benner, Peter; Mitchell, Tim

doi:10.1007/s10444-018-9592-x

Cited by 39 publications

(23 citation statements)

References 33 publications

(62 reference statements)

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“…Furthermore, it is intrinsically related to the Koopman operator analysis, see [31]. Moreover, DMD can be used to simultaneously identify an input operator [36,37], and an output operator [2,9]. Additionally in [18], the authors propose the DMD with control incorporation of quadratic-bilinear terms.…”

mentioning

confidence: 99%

Operator inference and physics-informed learning of low-dimensional models for incompressible flows

Benner¹,

Goyal²,

Heiland³

et al. 2021

etna

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Reduced-order modeling has a long tradition in computational fluid dynamics. The ever-increasing significance of data for the synthesis of low-order models is well reflected in the recent successes of data-driven approaches such as Dynamic Mode Decomposition and Operator Inference. With this work, we discuss an approach to learning structured low-order models for incompressible flow from data that can be used for engineering studies such as control, optimization, and simulation. To that end, we utilize the intrinsic structure of the Navier-Stokes equations for incompressible flows and show that learning dynamics of the velocity and pressure can be decoupled, thus, leading to an efficient operator inference approach for learning the underlying dynamics of incompressible flows. Furthermore, we demonstrate the performance of the operator inference in learning low-order models using two benchmark problems and compare with an intrusive method, namely proper orthogonal decomposition, and other data-driven approaches.

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confidence: 99%

Operator inference and physics-informed learning of low-dimensional models for incompressible flows

Benner¹,

Goyal²,

Heiland³

et al. 2021

etna

Self Cite

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show abstract

“…This ensures stability of solutions for future times as there are no growing modes. For input-output systems, DMD has also been modified through a postprocessing algorithm to generate a stable input-output model [15]. These methods show that DMD architectures can be imbued with advantageous stability properties for ROMs.…”

Section: Dynamic Mode Decompositionmentioning

confidence: 99%

7 Data-driven methods for reduced-order modeling

Brunton¹,

Kutz²

2020

Snapshot-Based Methods and Algorithms

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“…This model is tested in two variants: First, in a symmetric setting with zero flow speed v = 0, and second, in a non-normal setting with a flow speed v = 0.5. Due to the MIMO nature of the system we use the average system (see (4)) for the error indicator computation. This set of experiments is organized in the same manner as Section 4.1, but conducted for the prescribed projection errors ε ∈ {10 −2 , .…”

Section: Convection Benchmarkmentioning

confidence: 99%

Cross-Gramian-based dominant subspaces

Benner

2019

Adv Comput Math

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A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspaces projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.

show abstract

On reduced input-output dynamic mode decomposition

Cited by 39 publications

References 33 publications

Operator inference and physics-informed learning of low-dimensional models for incompressible flows

Operator inference and physics-informed learning of low-dimensional models for incompressible flows

7 Data-driven methods for reduced-order modeling

Cross-Gramian-based dominant subspaces

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