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Reduced-Order Models of Transport Phenomena.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Reduced-Order Models of Transport Phenomena./
作者:	Lu, Hannah (Hanqing).
面頁冊數:	1 online resource (226 pages)
附註:	Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
Contained By:	Dissertations Abstracts International84-04B.
標題:	Numerical analysis. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29342245click for full text (PQDT)
ISBN:	9798352602850

Reduced-Order Models of Transport Phenomena.
Lu, Hannah (Hanqing).

Reduced-Order Models of Transport Phenomena. - 1 online resource (226 pages)

Source: Dissertations Abstracts International, Volume: 84-04, Section: B.

Thesis (Ph.D.)--Stanford University, 2022.

Includes bibliographical references

Quantitative models of transport phenomena play a significant role in understanding and optimizing many energy-, environment-, and medicine-related processes. Despite remarkable advances in algorithm development and computer architecture, fineresolution/high-fidelity simulations remain a challenging and often unfeasible task due to the nonlinear nature of coupled transport phenomena, the complexity and heterogeneity of ambient environments, and the concomitant lack of sucient data needed to parameterize the models. The computational demands can be prohibitive, especially in optimization, control and uncertainty quantification problems, where thousands of simulations need to be run.Reduced-order models (ROMs) have been developed to obtain "cheap" yet accurate surrogates of high-fidelity models. The goal is to alleviate the expensive computational costs, while simultaneously capturing the underlying dynamic features. This dissertation addresses several challenges in construction of conventional ROMs for flow and transport problems, and introduces a physics-aware dynamic mode decomposition (DMD) framework to ameliorate the shortcomings of conventional ROMs. This framework supplements DMD, a data-driven tool that uses best linear approximations to construct ecient ROMs for complex systems, with physics-aware ingredients.The first part of this dissertation presents a study on prediction accuracy of DMD. While multiple numerical experiments demonstrated the power and eciency of DMD in representing data (i.e., in the interpolation mode), applications of DMD as a predictive tool (i.e., in the extrapolation mode) are scarce. This is due, in part, to the lack of rigorous error estimators for DMD-based predictions. We derive a theoretical error estimator for DMD extrapolation of numerical solutions, which allows one to monitor and control the errors associated with DMD-based ROMs approximating the physics-based models.In the second part of this dissertation, we demonstrate the shortcoming of conventional DMD methods (formulated within the Eulerian framework) for transport problems, in which sharp fronts play a dominant role in the dynamical systems. We propose a Lagrangian-based DMD method to overcome this so-called translational issues. This Lagrangian framework is valid only for smooth solutions, before a shock forms. After the shock formation, characteristic lines cross each other and the projection from the high-fidelity model (HFM) space to the low-fidelity model (LFM) space severely distorts the moving grid, resulting in numerical instabilities.In the third part of this dissertation, we address this grid distortion issue in ROMs of conservation laws with shock features. Then, we propose a shock-preserving DMD method based on a nonlinear hodograph transformation that relies on the conservation law at hand to recover a low-rank structure and overcome the numerical instability.In the fourth part of this dissertation, we propose an extended dynamic mode decomposition (xDMD) approach to cope with the potentially unknown sources/sinks in inhomogeneous partial di↵erential equations (PDEs). Our xDMD incorporates two new features, residual learning and bias identification, which are inspired by similar ideas in deep neural networks. Our theoretical error analysis demonstrates the guaranteed higher-order accuracy of xDMD relative to standard DMD.Finally, we introduce a new model-reduction framework - DRIPS (Dimension Reduction and Interpolation in Parameter Space) that combines DMD with reducedorder bases (ROBs) to construct ecient surrogates for parametric complex systems. We demonstrate that DRIPS obviates the need for both repeated access to expensive HFMs (the scourge of projection-based PROMs) and large amounts of data (the shortcoming of data-driven parametric ROMs).

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798352602850Subjects--Topical Terms:

517751
Numerical analysis.
Index Terms--Genre/Form:

542853
Electronic books.

Reduced-Order Models of Transport Phenomena.
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500 $a Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
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502 $a Thesis (Ph.D.)--Stanford University, 2022.
504 $a Includes bibliographical references
520 $a Quantitative models of transport phenomena play a significant role in understanding and optimizing many energy-, environment-, and medicine-related processes. Despite remarkable advances in algorithm development and computer architecture, fineresolution/high-fidelity simulations remain a challenging and often unfeasible task due to the nonlinear nature of coupled transport phenomena, the complexity and heterogeneity of ambient environments, and the concomitant lack of sucient data needed to parameterize the models. The computational demands can be prohibitive, especially in optimization, control and uncertainty quantification problems, where thousands of simulations need to be run.Reduced-order models (ROMs) have been developed to obtain "cheap" yet accurate surrogates of high-fidelity models. The goal is to alleviate the expensive computational costs, while simultaneously capturing the underlying dynamic features. This dissertation addresses several challenges in construction of conventional ROMs for flow and transport problems, and introduces a physics-aware dynamic mode decomposition (DMD) framework to ameliorate the shortcomings of conventional ROMs. This framework supplements DMD, a data-driven tool that uses best linear approximations to construct ecient ROMs for complex systems, with physics-aware ingredients.The first part of this dissertation presents a study on prediction accuracy of DMD. While multiple numerical experiments demonstrated the power and eciency of DMD in representing data (i.e., in the interpolation mode), applications of DMD as a predictive tool (i.e., in the extrapolation mode) are scarce. This is due, in part, to the lack of rigorous error estimators for DMD-based predictions. We derive a theoretical error estimator for DMD extrapolation of numerical solutions, which allows one to monitor and control the errors associated with DMD-based ROMs approximating the physics-based models.In the second part of this dissertation, we demonstrate the shortcoming of conventional DMD methods (formulated within the Eulerian framework) for transport problems, in which sharp fronts play a dominant role in the dynamical systems. We propose a Lagrangian-based DMD method to overcome this so-called translational issues. This Lagrangian framework is valid only for smooth solutions, before a shock forms. After the shock formation, characteristic lines cross each other and the projection from the high-fidelity model (HFM) space to the low-fidelity model (LFM) space severely distorts the moving grid, resulting in numerical instabilities.In the third part of this dissertation, we address this grid distortion issue in ROMs of conservation laws with shock features. Then, we propose a shock-preserving DMD method based on a nonlinear hodograph transformation that relies on the conservation law at hand to recover a low-rank structure and overcome the numerical instability.In the fourth part of this dissertation, we propose an extended dynamic mode decomposition (xDMD) approach to cope with the potentially unknown sources/sinks in inhomogeneous partial di↵erential equations (PDEs). Our xDMD incorporates two new features, residual learning and bias identification, which are inspired by similar ideas in deep neural networks. Our theoretical error analysis demonstrates the guaranteed higher-order accuracy of xDMD relative to standard DMD.Finally, we introduce a new model-reduction framework - DRIPS (Dimension Reduction and Interpolation in Parameter Space) that combines DMD with reducedorder bases (ROBs) to construct ecient surrogates for parametric complex systems. We demonstrate that DRIPS obviates the need for both repeated access to expensive HFMs (the scourge of projection-based PROMs) and large amounts of data (the shortcoming of data-driven parametric ROMs).
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