자료유형  

 학위논문

Control Number  

0017161498

International Standard Book Number  

9798382235219

Dewey Decimal Classification Number  

519

Main Entry-Personal Name  

Joshua Lamar Barnett.

Publication, Distribution, etc. (Imprint  

[S.l.] : Stanford University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

146 p.

General Note  

Source: Dissertations Abstracts International, Volume: 85-11, Section: B.

General Note  

Advisor: Charbel Farhat.

Dissertation Note  

Thesis (Ph.D.)--Stanford University, 2024.

Summary, Etc.  

요약Solving large-scale parameterized dynamical systems, which may be obtained through, for example, the discretization of partial differential equations, is foundationally important to many fields, including engineering. Oftentimes, these high-dimensional models are expensive to evaluate due, in part, to their large size; this expense may be exacerbated by repeated evaluations in a large-dimensional parameter space. Projection-based model order reduction is a framework that allows us to solve these high-dimensional models at a much lower cost in terms of computational resources. This is accomplished by collecting prior solutions associated with different parameter values obtained by exercising the high-dimensional model and forming a lower-dimensional subspace. Using this subspace, we can compute a new solution associated with an unsampled parameter value at (ideally) a much lower cost. This computational efficiency has significant implications for applications in simulation-driven design, optimal control, and uncertainty quantification, among others, all of which would be impractical, if not impossible, for truly large-scale problems without resorting to some form of surrogate modeling. In practice, however, projection-based reduced order models sometimes struggle to achieve this level of performance in problems that exhibit the well-known Kolmogorov barrier as is often encountered in first-order hyperbolic partial differential equations, e.g., Navier-Stokes equations. This dissertation presents dimension reduction techniques, the problem of the Kolmogorov barrier, why it remains a challenge for model reduction today, and discusses methods to solve it. Among these methods are two novel approaches presented in this dissertation: a data-driven quadratic approximation manifold as well as an arbitrarily nonlinear approximation manifold using artificial neural networks. With no sacrifice in accuracy, both achieve an order of magnitude improvement in wall clock time compared to the current state-of-the-art in projection-based model order reduction for industrial-grade flow problems.

Subject Added Entry-Topical Term  

Applied mathematics.

Subject Added Entry-Topical Term  

Mechanical engineering.

Index Term-Uncontrolled  

Partial differential equations

Index Term-Uncontrolled  

Projection-based model

Index Term-Uncontrolled  

Model reduction

Index Term-Uncontrolled  

Artificial neural networks

Added Entry-Corporate Name  

Stanford University.

Host Item Entry  

Dissertations Abstracts International. 85-11B.

Electronic Location and Access  

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Control Number  

joongbu:655458