时间：12月6日 (周五) 上午9:00-11:30

地点：中国人民大学崇德西楼815报告厅

主讲人简介

王典朋，北京理工大学数学与统计学院研究员，博士生导师。中国科学院系统与数学研究所博士后，曾先后访问佐治亚理工、香港科技大学，担任北京大数据协会常务理事、全国工业统计学教学研究会青年统计学家协会常务理事、中国现场统计研究会试验设计分会理事、全国工业统计学教学研究会理事。主要从事计算机试验设计、贝叶斯计算、不确定性量化、工业大数据等方向的研究。主持国家自然科学基金青年基金、面上项目和国家国防科技工业局先进星箭共性技术等项目多项，在Technometrics、Journal of Quality Technology、Statistica Sinica等统计学权威期刊上发表论文多篇。

Dr. Qian Xiao, currently a tenured associate professor in Dept. of Statistics, Shanghai Jiao Tong University. Prior to joining SJTU, he was a tenured associate professor in Dept. of Statistics at University of Georgia. He received his PhD from UCLA. He specializes in experimental design and analysis, uncertainty quantification and reinforcement learning. His research has been published in AOS, JASA, Biometrika and etc.

何煦，中国科学院数学与系统科学研究院系统科学研究所副研究员，本科毕业于北京大学数学科学学院，博士毕业于威斯康星大学麦迪逊分校统计系。主要研究方向包括实验设计，特别是计算机仿真实验的设计及分析。在Annals of Statistics，Journal of the American Statistical Association，Biometrika等杂志发表论文十余篇，曾主持国家自然科学基金委优秀青年基金、面上项目、青年基金。

内容概要

报告1：A nested singular value decomposition-based surrogate model for spatiotemporal flows

High-fidelity simulators have gained attention as effective alternatives to conducting physical experiments for understanding complex systems. However, these mathematical models are often time-consuming. While surrogate models, known as emulators, are useful for rapid simulations, they often fail to capture the dynamic information from flow fields, typically stored as tensors. This research proposes a reduced-basis method through nested decomposition to overcome these challenges. The relationships between the parameter-dependent coefficients and the simulator inputs are then modeled using Gaussian processes, which can be used to predict the coefficients at new inputs and subsequently recover the flow fields. The proposed novel method can significantly reduce the computational cost by decreasing the number of Gaussian processes. Some numerical experiments and two real-data case studies are conducted to demonstrate the superior performance of our method. The results show that, compared with existing methods, the new method can quickly yield accurate predictions of complex flows.

报告2：Penalized Additive Gaussian Process for Auto-Tuning of Quantitative and Qualitative Factors in Black-Box Systems

Factor screening and optimization of both quantitative and qualitative (QQ) factors are critical in several recent applications where evaluating black-box systems is resource-intensive or time-consuming. Moreover, some qualitative factors in QQ may involve many levels. Yet, most current screening methods focus on factors, but cannot identify important qualitative levels. To address these challenges, we propose a novel penalized additive Gaussian process (PAGP), featuring an interpretable additive covariance structure for QQ factors. It allows for sparsity penalties on the hyper-parameters of the covariance structure, which enables the identification of important qualitative levels. A tailored alternating direction method of multipliers is developed to optimize the L1 regularized likelihood, and a gradient-informed optimization approach using derivative information is proposed to accelerate PAGP modeling. We further establish an effective approach leveraging Shapley values for screening quantitative factors. Then, a Bayesian optimization (BO) approach leveraging the desirable uncertainty quantification of PAGP is proposed to optimize black-box systems with QQ factors. This PAGP-based Bayesian optimization can provide an interpretable importance attribution of factor levels during optimization. Simulations and real case studies illustrate the superior performance of the proposed methods compared to some state-of-the-art approaches.

报告3：Adaptive Grid Designs for Classifying Monotonic Binary Computer Simulations

This research is motivated by the need for effective classification in ice-breaking dynamic simulations, aimed at determining the conditions under which an underwater vehicle will break through the ice. This simulation is extremely time-consuming and yields deterministic, binary, and monotonic outcomes. Detecting the critical edge between the negative-outcome and positive-outcome regions with minimal simulation runs necessitates an efficient experimental design for selecting input values. Adaptive designs, which sequentially select input values based on obtained outcomes, outperform static designs significantly by eliminating redundant points without losing information. In this paper, we propose a new class of adaptive designs called adaptive grid designs. An adaptive grid is a sequence of grids with increasing resolution, such that lower resolution grids are proper subsets of higher resolution grids. By prioritizing simulation runs at lower resolution points and skipping redundant runs, adaptive grid designs require an order of magnitude fewer simulation runs to ensure a certain level of classification accuracy than the best possible static design and the same order of magnitude of runs as the best possible adaptive design. Numerical results across test functions, the road crash simulation, and the ice-breaking simulation validate the superiority of adaptive grid designs.