题目：Learning with Structure: Adaptive Gaussian Process Emulation via Sequential Lattice-Based Designs
时间：2025年6月9日 16:00-17:00
地点：williamhill威廉希尔官网 F103会议室
邀请人：李勇祥 副教授（工业工程与管理系）
Biography
Yuanyuan Lin received her B.Sc. in Statistics from Renmin University of China in 2016 and is expected to receive her Ph.D. from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, in 2025. Her current research focuses on Gaussian process modeling, experimental design, and computer experiments.
Abstract
Surrogate models are cost-effective approximations of time-consuming computer simulations. Adaptive designs are particularly effective for emulating heterogeneous functions with varying output variability. This work introduces a novel adaptive design method based on Gaussian process models and sequentially refined interleaved lattices. Our approach begins with an interleaved lattice-based initial design, and subsequent points are sequentially selected by optimizing a selection criterion over a dynamically enlarged candidate set, also structured by the underlying lattice. Our design and candidate set allocate denser points in high-variability regions and sparser points elsewhere; moreover, both maintain a reasonably low ratio between fill and separation distance across the whole input space. These features allow accurate modeling of complex patterns and further refinement in high-variability regions while avoiding excessive clustering and enhancing computational efficiency. Furthermore, we develop a robust lattice-informed trend estimation method suited for our non-uniformly distributed designs, and a new candidate selection criterion that effectively balances exploration and exploitation by approximating local Gaussian process variance. Comprehensive numerical experiments, including a challenging emulation of the chaotic Lorenz system, demonstrate that our method consistently outperforms existing approaches in prediction accuracy.
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