Bayesian Methods For Uncertainty Quantification
Computer codes simulating physical systems usually have responses that consist of a set of distinct outputs (e.g., velocity and pressure) that evolve also in space and time and depend on many unknown input parameters (e.g., physical constants, initial/boundary conditions, etc.). Furthermore, essential engineering procedures such as uncertainty quantification, inverse problems or design are notoriously difficult to carry out mostly due to the limited simulations available. The aim of this work is to introduce a fully Bayesian approach for treating these problems which accounts for the uncertainty induced by the infinite number of observations.
Bayesian; uncertainty quantification; computer surrogate; probability; limited simulations; expensive solvers
Zabaras, Nicholas John
Bindel, David S.; Vladimirsky, Alexander B.; Samorodnitsky, Gennady
Ph.D. of Applied Mathematics
Doctor of Philosophy
Dissertation or Thesis