题目：Liberating the Dimension: Construction of Quasi-Monte Carlo Rules for High-Dimensional Problems in Uncertainty Quantification

报告人：何志坚 教授（华南理工大学）

地点：致远楼101室

时间：2026年6月26日 星期五 16：00-17：00

Abstract：Quasi-Monte Carlo (QMC) integration over unbounded domains remains challenging due to the high dimensionality of sampling space and the boundary growth of the integrand. In applications such as uncertainty quantification (UQ), the dimension can reach hundreds or even thousands. To restore the efficiency of quadrature rules in high dimensions, constructive QMC methods like lattice rules have been successfully developed within the framework of weighted function spaces. In contrast to designing problem-specific quadrature points, we propose transforming the underlying integrand to accommodate the off-the-shelf scrambled nets (a construction-free randomized QMC method) via boundary-damping importance sampling (BDIS). We provide a rigorous analysis of the dimension-independent convergence rate of BDIS-based scrambled nets while covering a broader class of unbounded functions. By exploiting the dimension structure of the parametric input random field, the proposed quadrature rule achieves a dimension-independent mean squared error rate for elliptic PDEs in UQ. Numerical experiments demonstrate the effectiveness of the method for high-dimensional parameters as inputs.

报告人简介：何志坚，华南理工大学数学学院教授、博士生导师、副院长，广东省计算数学学会副理事长，CSIAM不确定性量化专业委员会委员，首批教育部哲学社会科学创新团队核心成员。2015年7月获清华大学理学博士学位，主要研究方向为随机计算方法与不确定性量化，尤其是拟蒙特卡罗方法的理论与应用。目前已发表SCI论文20余篇，其中15篇发表于《Mathematics of Computation》《SIAM Journal on Numerical Analysis》《SIAM Journal on Scientific Computing》《SIAM/ASA Journal on Uncertainty Quantification》《Journal of the Royal Statistical Society: Series B》等期刊。曾获新世界数学奖（ICCM毕业论文奖）银奖、广东省计算数学学会青年优秀学术成果奖一等奖，现任《Journal of Complexity》副主编。

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