Higher-order approximation manifolds for more efficient nonlinear projection-based model order reduction
Abstract/Contents
- Abstract
- Solving 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.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2024; ©2024 |
| Publication date | 2024; 2024 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Barnett, Joshua Lamar |
|---|---|
| Degree supervisor | Farhat, Charbel |
| Thesis advisor | Farhat, Charbel |
| Thesis advisor | Iaccarino, Gianluca |
| Thesis advisor | Kochenderfer, Mykel |
| Degree committee member | Iaccarino, Gianluca |
| Degree committee member | Kochenderfer, Mykel |
| Associated with | Stanford University, School of Engineering |
| Associated with | Stanford University, Department of Mechanical Engineering |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Joshua Barnett. |
|---|---|
| Note | Submitted to the Department of Mechanical Engineering. |
| Thesis | Thesis Ph.D. Stanford University 2024. |
| Location | https://purl.stanford.edu/kz939fz8483 |
Access conditions
- Copyright
- © 2024 by Joshua Lamar Barnett
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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