Title:
Novel Design and Surrogate Modeling Methods for Physical and Computer Experiments

Difan Song
Ph.D. Candidate in Industrial Engineering
H. Milton Stewart School of Industrial and Systems Engineering
Georgia Institute of Technology

Date:
Friday, June 19th, 2026

Time:
9:00 AM – 10:30 AM EDT

Location:
Georgia Freight Bureau Conference Room and Zoom

Zoom Link:
https://gatech.zoom.us/j/99429834697

Advisor/Chairperson:
Dr. Roshan V. Joseph, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Committee:
Dr. Roshan V. Joseph, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. C. F. Jeff Wu, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Xiao Liu, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Simon Mak, Department of Statistical Science, Duke University
Dr. Aaron Stebner, George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology
Dr. Eunhye Song, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Abstract:
Experiments are crucial to acquiring useful data across a variety of applications. Statistical experimental design and analysis have become indispensable tools for experimenters dealing with expensive physical and virtual experiments. This dissertation presents novel developments in design and modeling methodology that increase efficiency in tasks such as instrument optimization, factor screening, and active learning.

Chapter 1 investigates the problem of optimizing plasma x-ray radiation detectors in a magneto-inertial fusion experiment at Sandia National Laboratories. It is impossible to directly measure properties such as the temperature of the thermonuclear fusion plasma produced in these experiments because of the extreme environment and destructive nature of the experiment. Among other diagnostics, several detectors are placed with significant standoff from the fusion target to capture the x-rays emitted by the fusion plasma, which can be used to infer some of its properties. We develop methods based on A- and L-optimality criteria that are efficient to compute while explicitly accounting for the discrepancy between the simulation model and the inference model. The method allows us to find detector configurations that outperform an existing sampling-based optimization method while decreasing computational time by a factor of 50.

Chapter 2 explores efficient strategies for active learning of black-box computer experiments. We propose using the maximum one-factor-at-a-time (MOFAT) design as the initial design and a multiplicative inverse multiquadric (MIM) kernel for the correlation function. The ideas behind them are known in other fields, such as sensitivity analysis or kernel theory, but they never seem to have been used for active learning in computer experiments. We also propose an integrated MOFAT-MIM strategy that automatically incorporates screening in the model estimation step. We show that these strategies provide substantial improvement to the state-of-the-art methods for both emulation and optimization objectives.

Motivated by the effectiveness of the MOFAT designs in the previous chapter, Chapter 3 further explores screening designs for expensive black-box models that incorporate multiple types of factors, including nominal, ordinal, and discrete-numeric. We first identify the properties leading to optimal screening, where qualitative and quantitative factors should be treated differently. Based on these properties, we propose practical algorithms to efficiently construct MOFAT designs for all types of factors.

Finally, Chapter 4 proposes rational quadratic kriging, a kriging estimator that addresses the limitations of existing approaches: the mean reversion issue of ordinary kriging and the diverging variance issue of rational kriging. Through the rational quadratic kernel, we establish a connection between rational quadratic kriging and kernel regression. The connection allows us to prove desirable theoretical properties of the new estimator and further propose a novel estimation procedure that utilizes factor weights from kernel regression. We also derive expressions to enable efficient leave-one-out estimation and conformal prediction. Extensive simulations across both deterministic functions and noisy datasets show significant improvements in both prediction and uncertainty quantification.