A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations

Feng, Lihong; Fu, Guosheng; Wang, Zhu

doi:10.1007/s10915-021-01668-9

Cited by 6 publications

(9 citation statements)

References 25 publications

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“…The switch between FOM and ROM or between FOM and ROM-DEIM (but not among all the three) can be decided on the fly during the simulation. This hybrid simulation approach has been demonstrated for non-parametric and parametric Burger's equations and a nonlinear circuit problem (Feng et al, 2021). Therefore, in this article we propose to embed DEIM into the hybrid snapshot simulation, which enables model switch among FOM, ROM and ROM-DEIM.…”

Section: Ec 3910mentioning

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: Ec 3910mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

DEIM-embedded hybrid snapshot simulation for reduced order model generation

Bai

Wang

2022

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Section: Introductionmentioning

confidence: 99%

“…Adaptive reduced-order models (AROMs) [26,27,28,29,23,30] provide a different approach by continuously combining HDM and ROM operations. Predictive capabilities can be improved by alternating between HDM and ROM generated snapshots [26,27,28]. In [26,27], on-the-fly criteria relying on the reduced basis sufficiency is used to determine when to use the HDM or local ROM.…”

Section: Introductionmentioning

confidence: 99%

“…This methodology was successfully tested (factor of two speedup with an error inferior to 1%) on heat transfer [26] and fluid flow [27] problems. A similar approach relying on a more rigorous a posteriori error estimator to switch between the HDM and ROM is introduced in [28]. A different AROM method developed in [23] uses the adaptive discrete empirical interpolation method (ADEIM) [29] and rank-one updates to adapt the reduced basis.…”

Section: Introductionmentioning

confidence: 99%

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An Adaptive, Training-Free Reduced-Order Model for Convection-Dominated Problems Based on Hybrid Snapshots

Zucatti

Zahr

2023

Preprint

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An adaptive, training‐free reduced‐order model for convection‐dominated problems based on hybrid snapshots

Zucatti,

Zahr

2023

Numerical Methods in Fluids

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The vast majority of reduced‐order models (ROMs) first obtain a low dimensional representation of the problem from high‐dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately, convection‐dominated problems generally have a slowly decaying Kolmogorov ‐width, which makes obtaining an accurate ROM built solely from training data very challenging. The accuracy of a ROM can be improved through enrichment with HDM solutions; however, due to the large computational expense of HDM evaluations for complex problems, they can only be used parsimoniously to obtain relevant computational savings. In this work, we exploit the local spatial coherence often exhibited by these problems to derive an accurate, cost‐efficient approach that repeatedly combines HDM and ROM evaluations without a separate training phase. Our approach obtains solutions at a given time step by either fully solving the HDM or by combining partial HDM and ROM solves. A dynamic sampling procedure identifies regions that require the HDM solution for global accuracy and the reminder of the flow is reconstructed using the ROM. Moreover, solutions combining both HDM and ROM solves use spatial filtering to eliminate potential spurious oscillations that may develop. We test the proposed method on inviscid compressible flow problems and demonstrate speedups up to a factor of five.

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A FOM/ROM Hybrid Approach for Accelerating Numerical Simulations

Cited by 6 publications

References 25 publications

DEIM-embedded hybrid snapshot simulation for reduced order model generation

DEIM-embedded hybrid snapshot simulation for reduced order model generation

An Adaptive, Training-Free Reduced-Order Model for Convection-Dominated Problems Based on Hybrid Snapshots

An adaptive, training‐free reduced‐order model for convection‐dominated problems based on hybrid snapshots

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