From high-dimensional integration, intelligent optimization to surrogate model construction, the problem of sample point generation is widespread. With the increasing complexity and scale of modern engineering and scientific research problems, the demand for algorithms that can efficiently construct sample points in any dimension and shape space is increasingly urgent. This demand has promoted the rapid development of sampling technology in recent years. Starting from simple two-dimensional integration, this report expounds the uniform characteristics of low-deviation sample points, and focuses on the existing advanced uniform weight / non-uniform weight low-deviation sampling technology. The report further discusses the application of these low-bias sampling in practical engineering problems, including but not limited to uncertainty quantification, intelligent optimization and surrogate model construction. Through comparative analysis, the report demonstrates the significant contribution of these technologies in improving computational efficiency and accuracy.

Wu Feng is a full professor and doctoral supervisor in the School of Mechanics and Aerospace Engineering, Dalian University of Technology. He was on the editorial board of China Offshore Platform, Journal of Applied Mechanics and was a member of International Association of Computational Mechanics. He has published more than 80 journal articles (including IJMS, SEC, CMAME, MSSP, SIAM and other international top journals), 2 academic monographs, and has realized the achievement transformation of 2 million yuan. He has also won the second prize of national defense science and technology progress ; Dalian Youth Science and Technology Star ; Qian Weichang 's excellent thesis award, etc. He has been engaged in the research of fluid mechanics and computational mechanics for a long time. He has won 1 excellent teaching quality award from Dalian University of Technology, 3 excellent teaching quality awards, 1 second prize from Liaoning University Teaching Innovation Competition, 1 special prize from Liaoning Province Graduate Teaching Achievements, and 1 second prize from China National Graduate Teaching Achievements (2nd). His current research interests include computational symplectic mechanics and numerical calculation of uncertainty quantitative analysis.