Mathematical Sciences: Sampling Theory for Computer Experiments

这项研究涉及将统计学中的回归方法扩展到确定性但非常复杂的响应。 激励应用来自半导体工艺和器件设计。 在此应用程序中，有一些计算机程序可以模拟半导体器件的制造和操作的物理过程。 结果是，半导体的电特性可以根据其制造过程中的工艺规范进行计算。 程序运行时间较长，且描述过程的变量较多，因此有必要使用统计技术来找到输入变量的最佳设置。 人们可以在一组点上运行模拟器，并将模型拟合到计算值，以便对这些值的其他可能设置进行插值和外推。 通过以包含一定随机性的结构化方式选择点，可以估计模型中的不确定性。 该项目属于统计和概率领域，为半导体行业提供了许多统计应用程序。 该研究旨在探索一种反映计算机实验中一些标准设置的方法：许多维度、相对较少的数据点以及拟合复杂函数的需要。

This research involves the extension of regression methods in statistics to deterministic but very complicated responses. The motivating application is from semiconductor process and device design. In this application there are computer programs that simulate the physics of the fabrication and the operation of semiconductor devices. The result is that electrical properties of semiconductors can be computed as a function of the process specifications in their fabrication. A combination of long running times for the programs and a large number of variables that describe the process make it necessary to use statistical techniques to find optimal settings of the input variables. One can run the simulators at a set of points and fit the model to the computed values, for interpolation and extrapolation to other possible settings of those values. By choosing the points in a structured manner that incorporates some randomness, one can estimate the uncertainty in the model. This project is in the area of statistics and probability and offers a number of statistical applications to the semiconductor industry. The research is to explore an approach that reflects some standard settings in computer experiments: many dimensions, comparatively few data points, and a need to fit a complex function.