The advancements in science and technology in recent years have extended the scale of engineering problems. Discovery of new materials with desirable properties, drug discovery for treat-ment of disease, design of complex aerospace systems containing interactive subsystems, conducting experimental design of complex manufacturing processes, designing complex transportation systems all are examples of complex systems. The significant uncertainty and lack of knowledge about the underlying model due to the complexity necessitate the use of data for analyzing these systems. However, a huge time/economical expense involved in data gathering process avoids ac-quiring large amount of data for analyzing these systems. This dissertation is mainly focused on enabling design and decision making in complex uncertain systems. Design problems are pervasive in scientific and industrial endeavors: scientists design experiments to gain insights into physical and social phenomena, engineers design machines to execute tasks more efficiently, pharmaceutical researchers design new drugs to fight disease, and environ-mentalists design sensor networks to monitor ecological systems. All these design problems are fraught with choices, choices that are often complex and high-dimensional, with interactions that make them difficult for individuals to reason about. Bayesian optimization techniques have been successfully employed for experimental design of these complex systems. In many applications across computational science and engineering, engineers, scientists and decision-makers might have access to a system of interest through several models. These models, often referred to as "information sources", may encompass different resolutions, physics, and modeling assumptions, resulting in different "fidelity" or "skill" with respect to the quantities of interest. Examples of that include different finite-element models in design of complex mechanical structures, and various tools for analyzing DNA and protein sequence data in bioinformatics. Huge computation of the expensive models avoids excessive evaluations across design space. On the other hand, less expensive models fail to represent the objective function accurately. Thus, it is highly desirable to determine which experiment from which model should be conducted at each time point. We have developed a multi-information source Bayesian optimization framework capable of simultaneous selection of design input and information source, handling constraints, and making the balance between information gain and computational cost. The application of the proposed framework has been demonstrated on two different critical problems in engineering: 1) optimization of dual-phase steel to maximize its strength-normalized strain hardening rate in materials science; 2) optimization of NACA 0012 airfoil in aerospace. The design problems are often defined over a large input space, demanding large number of experiments for yielding a proper performance. This is not practical in many real-world problems, due to the budget limitation and data expenses. However, the objective function (i.e., experiment's outcome) in many cases might not change with the same rate in various directions. We have introduced an adaptive dimensionality reduction Bayesian optimization framework that exponentially reduces the exploration region of the existing techniques. The proposed framework is capable of identifying a small subset of linear combinations of the design inputs that matter the most relative to the objective function and taking advantage of the objective function representation in this lower dimension, but with richer information. A significant increase in the rate of optimization process has been demonstrated on an important problem in aerospace regarding aerostructural design of an aircraft wing modeled based on the NASA Common Research Model (CRM).
