DEIM reduced order model constructed by hybrid snapshot simulation

Bai, Feng; Wang, Yi

doi:10.1007/s42452-020-03958-7

Cited by 8 publications

(20 citation statements)

References 49 publications

(83 reference statements)

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“…Again it should be noted that in Eq. ( 25), DEIM is also applied to the source term D because of the temperature-dependent thermal capacitance M, which is different from our previous model (Bai and Wang, 2020b).…”

Section: Algorithm 2 the Deim Algorithmmentioning

confidence: 96%

“…For the sake of completeness, the corresponding FOM, ROM and ROM-DEIM will be briefly presented below following the generalized formulation in Eqs. ( 2), ( 3) and ( 7), and more detailed description can be found in (Bai and Wang, 2020b).…”

Section: Numerical Model Of Heat Transfermentioning

confidence: 99%

“…It switches the snapshot simulation between FOM and ROM by constructing the local ROM on-the-fly, and hence, reducing redundant information in the snapshot data and expediting the simulation without compromising data and ROM accuracy. In a later effort, a method was presented to utilize the snapshot data produced by the hybrid simulation to reconstruct the nonlinear terms, which generates ROM with DEIM interpolation for efficient online verification simulation (Bai and Wang, 2020b). Both prior efforts showed that the local ROM simulation in the hybrid method still takes an appreciable amount of computational time and can be enhanced for further acceleration.…”

Section: Introductionmentioning

confidence: 99%

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DEIM-embedded hybrid snapshot simulation for reduced order model generation

Bai

Wang

2022

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PurposeThe purpose of this paper is to establish an intelligent framework to generate the data representatives in snapshot simulation in order to construct the online reduced-order model based on the generated data information. It could greatly reduce the computational time in snapshot simulation and accelerate the computational efficiency in the real-time computation of reduced-order modeling.Design/methodology/approachThe snapshot simulation, which generates the data to construct reduced-order models (ROMs), usually is computationally demanding. In order to accelerate the snapshot generation, this paper presents a discrete element interpolaiton method (DEIM)-embedded hybrid simulation approach, in which the entire snapshot simulation is partitioned into multiple intervals of equal length. One of the three models: the full order model (FOM), local ROM, or local ROM-DEIM which represents a hierarchy of model approximations, fidelities and computational costs, will be adopted in each interval.FindingsThe outcome of the proposed snapshot simulation is an efficient ROM-DEIM applicable to various online simulations. Compared with the traditional FOM and the hybrid method without DEIM, the proposed method is able to accelerate the snapshot simulation by 54.4%–63.91% and 10.5%–27.85%, respectively. In the online simulation, ROM-DEIM only takes 4.81%–8.56% of the computational time of FOM, while preserving excellent accuracy (with relative error <1%).Originality/value1. A DEIM-embedded hybrid snapshot simulation methodology is proposed to accelerate snapshot data generation and reduced-order model (ROM)-DEIM development. 2. The simulation alternates among FOM, ROM and ROM-DEIM to adaptively generate snapshot data of salient subspace representation while minimizing computational load. 3. The DEIM-embedded hybrid snapshot approach demonstrates excellent accuracy (<1% error) and computational efficiency in both online snapshot simulation and online ROM-DEIM verification simulation.

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Section: Algorithm 2 the Deim Algorithmmentioning

confidence: 96%

Section: Numerical Model Of Heat Transfermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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DEIM-embedded hybrid snapshot simulation for reduced order model generation

Bai

Wang

2022

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“…They explained why in some applications this sensitivity is a concern while in others it is not. Therefore, hybrid methods (FOM/ROM switched back and forth) are commonly used in practice [1,10,23,28]. However, the savings are not remarkable.…”

Section: Introductionmentioning

confidence: 99%

A new reduced order model of linear parabolic PDEs

Walkington¹,

Weber²,

Zhang³

2022

Preprint

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How to build an accurate reduced order model (ROM) for multidimensional time dependent partial differential equations (PDEs) is quite open. In this paper, we propose a new ROM for linear parabolic PDEs. We prove that our new method can be orders of magnitude faster than standard solvers, and is also much less memory intensive. Under some assumptions on the problem data, we prove that the convergence rates of the new method is the same with standard solvers. Numerical experiments are presented to confirm our theoretical result.

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“…Several approaches have been pursued to tackle these issues. To save the computational cost for snapshot generation, a hybrid snapshot simulation methodology was proposed to accelerate the high-quality data generation for the proper orthogonal decomposition (POD) ROM development in [3,2]. In this approach, the simulation alternates between full-order model (FOM) and local ROM based on criteria related to the singular value distribution and the magnitude of POD basis coefficients.…”

Section: Introductionmentioning

confidence: 99%

A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations

Feng¹,

Fu²,

Wang³

2021

Preprint

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The basis generation in reduced order modeling usually requires multiple high-fidelity largescale simulations that could take a huge computational cost. In order to accelerate these numerical simulations, we introduce a FOM/ROM hybrid approach in this paper. It is developed based on an a posteriori error estimation for the output approximation of the dynamical system. By controlling the estimated error, the method dynamically switches between the full-order model and the reduced-oder model generated on the fly. Therefore, it reduces the computational cost of a high-fidelity simulation while achieving a prescribed accuracy level. Numerical tests on the non-parametric and parametric PDEs illustrate the efficacy of the proposed approach.

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DEIM reduced order model constructed by hybrid snapshot simulation

Cited by 8 publications

References 49 publications

DEIM-embedded hybrid snapshot simulation for reduced order model generation

DEIM-embedded hybrid snapshot simulation for reduced order model generation

A new reduced order model of linear parabolic PDEs

A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations

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