Browsing by Author "Xie, Guangrui"

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    Multi-Resolution Sensitivity Analysis of Model of Immune Response to Helicobacter pylori Infection via Spatio-Temporal Metamodeling
    Chen, Xi; Wang, Wenjing; Xie, Guangrui; Hontecillas, Raquel; Verma, Meghna; Leber, Andrew; Bassaganya-Riera, Josep; Abedi, Vida (Frontiers, 2019-02-05)
    Computational immunology studies the interactions between the components of the immune system that includes the interplay between regulatory and inflammatory elements. It provides a solid framework that aids the conversion of pre-clinical and clinical data into mathematical equations to enable modeling and in silico experimentation. The modeling-driven insights shed lights on some of the most pressing immunological questions and aid the design of fruitful validation experiments. A typical system of equations, mapping the interaction among various immunological entities and a pathogen, consists of a high-dimensional input parameter space that could drive the stochastic system outputs in unpredictable directions. In this paper, we perform spatio-temporal metamodel-based sensitivity analysis of immune response to Helicobacter pylori infection using the computational model developed by the ENteric Immune SImulator (ENISI). We propose a two-stage metamodel-based procedure to obtain the estimates of the Sobol’ total and first-order indices for each input parameter, for quantifying their time-varying impacts on each output of interest. In particular, we fully reuse and exploit information from an existing simulated dataset, develop a novel sampling design for constructing the two-stage metamodels, and perform metamodel-based sensitivity analysis. The proposed procedure is scalable, easily interpretable, and adaptable to any multi-input multi-output complex systems of equations with a high-dimensional input parameter space.
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    Robust and Data-Efficient Metamodel-Based Approaches for Online Analysis of Time-Dependent Systems
    Xie, Guangrui (Virginia Tech, 2020-06-04)
    Metamodeling is regarded as a powerful analysis tool to learn the input-output relationship of a system based on a limited amount of data collected when experiments with real systems are costly or impractical. As a popular metamodeling method, Gaussian process regression (GPR), has been successfully applied to analyses of various engineering systems. However, GPR-based metamodeling for time-dependent systems (TDSs) is especially challenging due to three reasons. First, TDSs require an appropriate account for temporal effects, however, standard GPR cannot address temporal effects easily and satisfactorily. Second, TDSs typically require analytics tools with a sufficiently high computational efficiency to support online decision making, but standard GPR may not be adequate for real-time implementation. Lastly, reliable uncertainty quantification is a key to success for operational planning of TDSs in real world, however, research on how to construct adequate error bounds for GPR-based metamodeling is sparse. Inspired by the challenges encountered in GPR-based analyses of two representative stochastic TDSs, i.e., load forecasting in a power system and trajectory prediction for unmanned aerial vehicles (UAVs), this dissertation aims to develop novel modeling, sampling, and statistical analysis techniques for enhancing the computational and statistical efficiencies of GPR-based metamodeling to meet the requirements of practical implementations. Furthermore, an in-depth investigation on building uniform error bounds for stochastic kriging is conducted, which sets up a foundation for developing robust GPR-based metamodeling techniques for analyses of TDSs under the impact of strong heteroscedasticity.
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    A Uniform Error Bound for Stochastic Kriging: Properties and Implications on Simulation Experimental Design
    Chen, Xi; Zhang, Yutong; Xie, Guangrui; Zhang, Jingtao (ACM, 2024-08)
    In this work, we propose a method to construct a uniform error bound for the SK predictor. In investigating the asymptotic properties of the proposed uniform error bound, we examine the convergence rate of SK's predictive variance under the supremum norm in both fixed and random design settings. Our analyses reveal that the large-sample properties of SK prediction depend on the design-point set determined by the design-point sampling scheme and the budget allocation scheme adopted. Appropriately controlling the order of noise variances through budget allocation is crucial for achieving a desirable convergence rate of SK's approximation error, as quantified by the uniform error bound, and for maintaining SK's numerical stability. Moreover, we investigate the impact of noise variance estimation on the uniform error bound's performance theoretically and numerically. Through comprehensive numerical evaluations, we demonstrate the superiority of the proposed uniform bound to the Bonferroni correction-based simultaneous confidence interval under various experimental settings.