Bayesian inference of stochastic dynamical models
Author(s)Lu, Peter Guang Yi
Massachusetts Institute of Technology. Department of Mechanical Engineering.
Pierre F.J. Lermusiaux.
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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.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 165-175).
DepartmentMassachusetts Institute of Technology. Department of Mechanical Engineering.
Massachusetts Institute of Technology