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Development of Improved Parameterizations and Nonlinear Regression for Reduced-Order Modeling in Combustion.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Development of Improved Parameterizations and Nonlinear Regression for Reduced-Order Modeling in Combustion./
Author:	Armstrong, Elizabeth.
Description:	1 online resource (188 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-02, Section: B.
Contained By:	Dissertations Abstracts International85-02B.
Subject:	Chemical engineering. -
Online resource:	click for full text (PQDT)
ISBN:	9798380130059

Development of Improved Parameterizations and Nonlinear Regression for Reduced-Order Modeling in Combustion.
Armstrong, Elizabeth.

Development of Improved Parameterizations and Nonlinear Regression for Reduced-Order Modeling in Combustion. - 1 online resource (188 pages)

Source: Dissertations Abstracts International, Volume: 85-02, Section: B.

Thesis (Ph.D.)--The University of Utah, 2023.

Includes bibliographical references

Reduced-order modeling is a common approach to enabling computationally efficient simulations of high-dimensional, dynamical systems such as those found in combustion. These models involve choosing a small set of parameters to represent a high-dimensional system alongside a tabulation or regression method for reconstructing quantities of interest (QoIs) over the chosen parameters. Accurate reconstruction of QoIs, which may include non-linear functions of the original parameters, is a key factor in the success of a low-dimensional model during transport in a simulation. This not only depends on the regression, but also on the projection itself.The advancements proposed herein improve the quality and accuracy of both the set of chosen parameters and the reconstruction of QoIs that follows. Projecting high-dimensional states onto a set of low-dimensional parameters can introduce undesirable features such as sharp gradients or non-uniqueness in a QoI, which pose difficulties for reconstruction methods. Therefore, a new quantitative metric is proposed for optimizing the low-dimensional model parameters through assessing manifold quality based on QoI feature sizes. Reconstruction is then traditionally performed with interpolants, but these suffer from exponential growth in memory with dimensionality. A comparison with more recently employed feedforward artificial neural networks (ANNs) highlights the ANN shortcomings in reconstruction accuracy and training reliability despite having advantages elsewhere. Regression accuracy can be optimized using the recently introduced partition of unity networks (POUnets), which learn a mesh-free partitioning of space alongside localized polynomial approximations. POUnets are shown to achieve interpolant levels of accuracy with the low memory footprints of neural networks.As a final demonstration, an in-depth analysis of the processes involved with constructing and training reduced-order models using the contributions above is provided. Discussions are centered around the challenges of ensuring a successful evolution of a high-dimensional system in a low-dimensional space using data-based models. The importance of choosing appropriate training data, projections, and reconstruction methods is highlighted in both one- and two-dimensional direct numerical simulations of a non-premixed laminar flame. A new approach to training QoI-based projections is also proposed, which is shown to improve model behavior in simulation, and the effects of projections on stiffness are explored.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380130059Subjects--Topical Terms:

555952
Chemical engineering.
Subjects--Index Terms:

QoIsIndex Terms--Genre/Form:

554714
Electronic books.

Development of Improved Parameterizations and Nonlinear Regression for Reduced-Order Modeling in Combustion.
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520 $a Reduced-order modeling is a common approach to enabling computationally efficient simulations of high-dimensional, dynamical systems such as those found in combustion. These models involve choosing a small set of parameters to represent a high-dimensional system alongside a tabulation or regression method for reconstructing quantities of interest (QoIs) over the chosen parameters. Accurate reconstruction of QoIs, which may include non-linear functions of the original parameters, is a key factor in the success of a low-dimensional model during transport in a simulation. This not only depends on the regression, but also on the projection itself.The advancements proposed herein improve the quality and accuracy of both the set of chosen parameters and the reconstruction of QoIs that follows. Projecting high-dimensional states onto a set of low-dimensional parameters can introduce undesirable features such as sharp gradients or non-uniqueness in a QoI, which pose difficulties for reconstruction methods. Therefore, a new quantitative metric is proposed for optimizing the low-dimensional model parameters through assessing manifold quality based on QoI feature sizes. Reconstruction is then traditionally performed with interpolants, but these suffer from exponential growth in memory with dimensionality. A comparison with more recently employed feedforward artificial neural networks (ANNs) highlights the ANN shortcomings in reconstruction accuracy and training reliability despite having advantages elsewhere. Regression accuracy can be optimized using the recently introduced partition of unity networks (POUnets), which learn a mesh-free partitioning of space alongside localized polynomial approximations. POUnets are shown to achieve interpolant levels of accuracy with the low memory footprints of neural networks.As a final demonstration, an in-depth analysis of the processes involved with constructing and training reduced-order models using the contributions above is provided. Discussions are centered around the challenges of ensuring a successful evolution of a high-dimensional system in a low-dimensional space using data-based models. The importance of choosing appropriate training data, projections, and reconstruction methods is highlighted in both one- and two-dimensional direct numerical simulations of a non-premixed laminar flame. A new approach to training QoI-based projections is also proposed, which is shown to improve model behavior in simulation, and the effects of projections on stiffness are explored.
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