| dc.description.abstract | This dissertation investigates the uncertainty quantification of prediction in high-dimensional problems. A systematic approach including adaptive surrogate modeling, discrepancy modeling and uncertainty propagation for high-dimensional input and output is studied in this dissertation. The dissertation has three objectives: surrogate modeling for high-dimensional input and output, adaptive improvement of the surrogate model, and discrepancy modeling in Bayesian calibration and uncertainty quantification (UQ) in predictions of unobserved outputs. Several methods for reducing the output dimension are explored and compared, namely, singular value decomposition (SVD), random projection, randomized SVD and diffusion maps; and two methods for the input dimension are investigated: variance-based sensitivity analysis and active subspace discovery. This is followed by the construction of Gaussian process and simple regression surrogate models in the low-dimensional latent space. Using an active learning function introduced in the latent space that properly considers all subspaces, new physics-based model runs are proposed to adaptively improve the surrogate model. Model discrepancy is then introduced through additive terms to the surrogate models in the latent space. With measurement data, the model discrepancy is calibrated along with observation error. The calibrated quantities are used for uncertainty quantification of predictions of unobserved system outputs. | |
