Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Thesis_WLR_Final.pdf (11.05 MB)

ETD Abstract Container

Abstract Header

Surrogate Markov Models for Validation and Comparative Analysis of Proper Orthogonal Decomposition and Dynamic Mode Decomposition Reduced Order Models

Rickman, William Lucas
http://orcid.org/0009-0004-2801-8023
http://rave.ohiolink.edu/etdc/view?acc_num=miami1733750547445008

Abstract Details

2025, Master of Science, Miami University, Mechanical and Manufacturing Engineering.
Reduced order modeling (ROM) methods, such as those based upon Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD), offer data-based turbulence modeling with potential applications for flow control. While these models are often cheaper than numerical approaches, their results require validation with source data. Within the literature, the metrics and standards used to validate these models are often inconsistent. Chabot (2014) produced a data-driven framework for validating these ROMs that used surrogate Markov models (SMMs) to compare how the system dynamics evolved rather than how any single metric evolved. These SMMs were constructed by clustering the flow data into different states of suitably similar flow fields, and the Markov model then mapped how likely each state was to transition into another. While this method was successful, there persisted an amount of uncertainty in how the outlier states within this clustering scheme were determined. Additionally, the study only examined the application of this procedure to POD-Galerkin ROMs. This study aims to tie the outlier state determination directly to the models’ parent data. The study will also apply this procedure to ROMs generated from DMD to investigate how this framework's effectiveness carries over to different classes of ROMs.
Edgar Caraballo (Advisor)
Andrew Sommers (Committee Member)
Mehdi Zanjani (Committee Member)
169 p.
Aerospace Engineering; Fluid Dynamics; Mathematics; Mechanical Engineering; Statistics
fluid dynamics; validation; reduced order models; proper orthogonal decomposition; dynamic mode decomposition; optimized dynamic mode decomposition; Markov model; surrogate Markov model; clustering; Gaussian mixture modeling; turbulence; linear models; Koopman theory; Galerkin projection; eddy viscosity models

Recommended Citations

Citations

  • Rickman, W. L. (2025). Surrogate Markov Models for Validation and Comparative Analysis of Proper Orthogonal Decomposition and Dynamic Mode Decomposition Reduced Order Models [Master's thesis, Miami University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=miami1733750547445008

    APA Style (7th edition)

  • Rickman, William. Surrogate Markov Models for Validation and Comparative Analysis of Proper Orthogonal Decomposition and Dynamic Mode Decomposition Reduced Order Models. 2025. Miami University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=miami1733750547445008.

    MLA Style (8th edition)

  • Rickman, William. "Surrogate Markov Models for Validation and Comparative Analysis of Proper Orthogonal Decomposition and Dynamic Mode Decomposition Reduced Order Models." Master's thesis, Miami University, 2025. http://rave.ohiolink.edu/etdc/view?acc_num=miami1733750547445008

    Chicago Manual of Style (17th edition)

miami1733750547445008
1
© 2024, all rights reserved.
This open access ETD is published by Miami University and OhioLINK.