Mathematical Sciences: Archetypal Analysis of Complex Spatio-Temporal Data

这项工作得到了女性科学家和工程师研究计划资助奖的支持。当前动力系统领域的一个主要研究领域是对复杂时空动力学的理解、预测和建模。随着高速、大容量计算机的出现，更复杂的统计学方法在分析动力系统数据方面变得实用起来。该项目的目标之一是比较和对比Karhunen-Loeve （KL）分解和原型两种方法在几个实验动力系统中的应用，包括物理和数值。另一个目标是提出一种方法，该方法建立在翻译连贯结构的数据原型分析的基础上，通过客观的方式找到与移动结构一起移动的原型。提取结构本身的形状（或者可能是形状，如果结构本身是变化的，以及翻译）以及关于结构如何在空间域中移动的信息。第三个目标是确定使用原型作为基础的可行性，在此基础上执行控制方程的伽辽金投影（当它们存在时），用于建模目的。美国国家科学基金会的任务是确保国家科学事业的活力，包括关注科学和工程领域人力资源基础的质量、组成、分布和有效性。在此背景下，基金会致力于提高目前女性在科学和工程事业中的参与率，总体而言，并积极参与其所有项目。研究计划奖助金的设立：(1)帮助增加新的女性研究人员参与NSF的研究项目；(2)促进先前未获得独立联邦研究经费的妇女开展与竞争性研究项目和建议有关的初步研究和其他活动。研究计划补助金是一次性奖励，可用于初步工作，以确定拟议的调查线的可行性，和/或用于其他活动，将促进提案的发展。

9510284 Stone This work is supported by a Research Planning Grant for Women Scientists and Engineers Award. A major area of current interest in the field of dynamiaal systems is the understanding, prediction, and modeling of complex spatio-temporal dynamics. With the advent of high-speed, large capacity computers, more complex methods from statistics have become practical in the analysis of data from dynamical systems. One of the goals of this project is to compare and contrast two methods, Karhunen-Loeve (KL) decomposition and Archetypes, in their application to several experimental dynamical systems, both physical and numerical. Another goal is to propose a method that builds on Archetypal analysis for data with translating coherent structures, by finding archetypes that move with the traveling structure, in an objective manner. The shape of the structure itself is extracted (or possibly shapes, if the structure itself is varying as well as translating) as well as information on how the structure is moving across the spatial domain. A third goal is to determine the feasibility of using archetypes as a basis upon which to perform a Galerkin projection of the governing equations (when they exist), for modeling purposes. The National Science Foundation's mandate to ensure the vitality of the Nation's scientific enterprise includes concern for the quality, composition, distribution and effectiveness of the human resource base in science and engineering. Within this context, the Foundation is committed to enhancing the current rate of participation of women in science and engineering careers, in general, and as active participants in all of its programs. Research Planning Grant awards are made: (1) to help increase the number of new women investigators participating in NSF's research programs; and, (2) to facilitate preliminary studies and other activities related to the development of competitive research projects and proposals by women who have not previously had independent Federal research funding. Research Planning Grants are one-time awards that may be used for preliminary work to determine the feasibility of a proposed line of inquiry, and/or for other activities that will facilitate proposal development.