2026-09-18T17:30:09Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/792652022-01-13T07:54:05Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Pierre F.J. Lermusiaux.
Lu, Peter Guang Yi
Massachusetts Institute of Technology. Department of Mechanical Engineering.
Massachusetts Institute of Technology. Department of Mechanical Engineering
2013-06-17T19:51:45Z
2013-06-17T19:51:45Z
2013
2013
http://hdl.handle.net/1721.1/79265
846627771
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 165-175).
A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.
by Peter Lu.
S.M.
175 p.
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mechanical Engineering.
Bayesian inference of stochastic dynamical models
Thesis
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Publication
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<Abstract>A new methodology for Bayesian inference of stochastic dynamical models is developed. The methodology leverages the dynamically orthogonal (DO) evolution equations for reduced-dimension uncertainty evolution and the Gaussian mixture model DO filtering algorithm for nonlinear reduced-dimension state variable inference to perform parallelized computation of marginal likelihoods for multiple candidate models, enabling efficient Bayesian update of model distributions. The methodology also employs reduced-dimension state augmentation to accommodate models featuring uncertain parameters. The methodology is applied successfully to two high-dimensional, nonlinear simulated fluid and ocean systems. Successful joint inference of an uncertain spatial geometry, one uncertain model parameter, and [Omicron](105) uncertain state variables is achieved for the first. Successful joint inference of an uncertain stochastic dynamical equation and [Omicron](105) uncertain state variables is achieved for the second. Extensions to adaptive modeling and adaptive sampling are discussed.</Abstract>
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