Graduation Year

2026

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Lu Lu, Ph.D.

Committee Member

Kandethody Ramachandran, Ph.D.

Committee Member

Seung-Yeop Lee, Ph.D.

Committee Member

Jiwoong Kim, Ph.D.

Committee Member

Peng Chen, Ph.D.

Keywords

Computer experiments, Hierarchical clustering, Input-response, Non-uniform, Pareto front, Space-filling design, Response Uncertainty, Mahalanobis Distance, Maximin Distance, Minimax Distance

Abstract

This dissertation presents three methodological advancements to improve the construction of space-filling designs for meeting different needs of computer experiments. Traditional space-filling designs focus on achieving uniform coverage in the input space, ensuring that design points are spread evenly throughout. However, in some scientific and engineering applications, varied density of design points may be desired for more efficient data collection when prior knowledge implies different emphases. In other cases, ensuring good coverage and/or spread of the response values allows better performance of fitted models in the next stage of applications. Many processes involve variation in response values. Therefore, incorporating variation in the response space can result in more realistic design with robust performance in real world applications. In addition, as the dimensionality and complexity of experiments increase, the computational cost and time required to generate high-quality designs increase substantially and hence call for more efficient algorithms for generating desired space-filling designs.

This dissertation addresses these challenges and proposes methods and/or algorithms for generating new space-filling designs of desired characteristics. In Chapter 2, we propose the Input–Response Space-Filling Design with Uncertainty (IRSFwU), a new approach that enhances the Input-Response Space-Filling (IRSF) designs (Lu and Anderson Cook, 2021a) and incorporates subject matter expert (SME) knowledge and associated response uncertainty into the design construction. The method introduces an uncertainty-adjusted distance metric to measure the spread of possible response values while considering uncertainty. It also develops a modified Pareto front construction algorithm to generate a suite of non-dominated designs that balance coverage in both the input and response spaces with a preference on design points associated with lower response uncertainty. In Chapter 3, we address the computational challenges that are faced by the original non-uniform space-filling (NUSF) designs (Lu et al., 2021), which allow users to emphasize specific regions of interest but are often computationally intensive, especially for higher dimensional problems. We develop the Quick Non-Uniform Space-Filling (QNUSF) method, which leverages hierarchical clustering and strategic point selection to drastically reduce computational time. To expand its applications, we developed two variants, maximin and minimax QNUSF, which offer flexibility in prioritizing different space-filling characteristics emphasizing spread or coverage of design points for different applications. The new algorithms also support both continuous and discrete design spaces and adapt easily to regular design space or irregular domains that subject to constraints. Chapter 4 introduces the Quick Input–Response Space-Filling (QIRSF) method, a fast and scalable alternative to traditional IRSF designs (Lu and Anderson Cook, 2021a) to balance the input and response space-filling characteristics. QIRSF efficiently constructs Pareto fronts of designs that balance input and response space coverage to different degrees. Additionally, a new graphical tool, the Distance Fractional Design Space (DFDS) plot, is proposed to help visualize and compare design performance for better decision-making. In summary, these contributions offer flexible, knowledge-informed, and computationally efficient tools for constructing versatile space-filling designs tailored to more complex, higher-dimensional, and realistic experimental scenarios.

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