PhD, University of Cincinnati, 2022, Arts and Sciences: Mathematical Sciences

The focus of this thesis is to use deep learning methods for computer model calibration and uncertainty quantification. Computer model calibration is the process of combining information from computer model outputs and observation data to make inference about unknown input parameters of the computer model. The framework for calibration involves an emulation step which faces computational issues when data is high dimensional and a calibration step which faces the inferential issues due to the nonidentifiability between the input parameters and data-model discrepancy. The main aim of this thesis is to address these computational and inferential issues using deep learning methods. This thesis contribute in the field of computer model calibration in the following way: 1) Developing a new inverse model-based computer model calibration framework that utilizes the feature extraction ability of deep neural network to efficiently handle high dimensional data while filtering out the effects of data-model discrepancy. 2) Formulating a computationally efficient generative deep learning model-based emulation method for large spatial data. 3) Siamese neural network and approximate Bayesian computation-based calibration method that can efficiently solve the issue of data-model discrepancy. The proposed methods have been successfully applied to calibrate important climate models such as Weather Research and Forecasting Model (WRF-Hydro) and University of Victoria Earth System Climate Model(UVic ESCM).

Committee: Won Chang Ph.D. (Committee Member); Siva Sivaganesan Ph.D. (Committee Member); Bledar Konomi Ph.D. (Committee Member); Emily Kang Ph.D. (Committee Member) Subjects: Statistics

PhD, University of Cincinnati, 2022, Arts and Sciences: Mathematical Sciences

Expensive computer models (simulators) are frequently used to simulate the behavior of a complex system in many scientific fields because an explicit experiment is very expensive or dangerous to conduct. Usually, only a limited number of computer runs are available due to limited sources. Therefore, one desires to use the available runs to construct an inexpensive statistical model, an emulator. Then the constructed statistical model can be used as a surrogate for the computer model. Building an emulator for high dimensional outputs with the existing standard method, the Gaussian process model, can be computationally infeasible because it has a cubic computational complexity that scales with the total number of observations. Also, it is common to impose restrictions on the covariance matrix of the Gaussian process model to keep computations tractable. This work constructs a flexible emulator based on a deep neural network (DNN) with feedforward multilayer perceptrons (MLP). High dimensional outputs and limited runs can pose considerable challenges to DNN in learning a complex computer model's behavior. To overcome this challenge, we take advantage of the computer model's spatial structure to engineer features at each spatial location and then make the training of DNN feasible. Also, to improve the predictive performance and avoid overfitting, we adopt a data augmentation technique into our method. Finally, we apply our approach using data from the UVic ESCM model and the PSU3D-ICE model to demonstrate good predictive performance and compare it with an existing state-of-art emulation method.

Committee: Won Chang Ph.D. (Committee Member); Xia Wang Ph.D. (Committee Member); Emily Kang Ph.D. (Committee Member) Subjects: Statistics