Collaborative Research: Multi-Scale Modeling of Non-Gaussian Random Fields

合作研究：非高斯随机场的多尺度建模

基本信息

批准号：
1811279
负责人：
Tomoko Matsuo
金额：
$ 5万
依托单位：
University of Colorado at Boulder
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-09-01 至 2021-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811279&HistoricalAwards=false
关键词：
Collaborative Research Multi Scale Modeling

项目摘要

Data collected on various environmental, geophysical and meteorological processes often exhibit different modes of variability, especially at different scales. An accurate description of the features of the fluctuations in these data can improve scientific understanding of the physical phenomena. Development of new statistical tools for modeling such geophysical processes can also enhance the ability to monitor and predict the impact of their fluctuations on communication systems and sensory networks. Despite the ubiquity of such data, few statistical methodologies are currently available to describe such spatiotemporal scalar and vector random fields globally on a spherical domain. One key objective of this project is to propose a multiscale approach for constructing non-Gaussian random fields on a sphere, that on the one hand provides a flexible mathematical framework for modeling, and on the other hand, enables one to fit these models by using modern computational tools. A further objective is to extend the methodologies to deal with data observed on graphs and networks. The project also aims to demonstrate the effectiveness of the proposed methodologies in enhancing scientific understanding of geophysical processes by analyzing ground-based and satellite-based measurements of the earth's magnetic fields. The proposed statistical framework for spherical processes is based on the idea of multiresolution analysis on a sphere. In this application, a class of needlet frames on the unit sphere is utilized as a building block to construct spatio-temporal scalar and vector fields on the unit sphere that satisfy natural physical constraints such as being curl-free or divergence-free, thereby enabling a flexible approach to approximating physical processes. Parametric statistical models are proposed to model random vector fields on the unit sphere and spherical shells. These random fields are represented in terms of vectorial needlets and can exhibit non-Gaussian features. A suite of methodologies is proposed under this modeling paradigm to analyze and predict large-scale spatiotemporal scalar and vector processes arising in geophysics, such as ground and satellite based measurements on the earth's main magnetic field or on ionospheric electro-magnetic fields. Theoretical questions related to the structure and properties of the proposed vectorial needlets and the random vector fields represented by them are also investigated. The flexible framework of modeling random fields through multiresolution analysis is further exploited to construct non-Gaussian processes on graphs by means of graph spectral wavelets. This collaborative project requires bringing together skills and knowledge from disparate areas such as multiresolution analysis, spatial statistics, spectral graph theory, Bayesian and large-scale computation, space physics, and geophysics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在各种环境，地球物理和气象过程上收集的数据通常表现出不同的可变性方式，尤其是在不同的尺度下。对这些数据波动的特征的准确描述可以改善对物理现象的科学理解。开发用于建模这种地球物理过程的新统计工具还可以增强监测和预测其波动对通信系统和感觉网络的影响的能力。尽管此类数据无处不在，但目前几乎没有统计方法可以在球形域上在全球范围内描述这种时空标量和矢量随机场。该项目的一个关键目的是提出一种多尺度方法，用于在球体上构建非高斯随机字段，一方面，它为建模提供了灵活的数学框架，另一方面，可以通过使用现代计算工具来拟合这些模型。一个进一步的目标是扩展处理图和网络上观察到的数据的方法。该项目还旨在通过分析基于地面的地球磁场的测量值来证明所提出的方法学对增强地球物理过程的科学理解的有效性。球形过程的拟议统计框架基于对球体的多分辨率分析的概念。在此应用程序中，单位球上的一类登顶框架被用作构建时空标量和矢量场的组成部分，在单位球上构建满足自然物理约束的满足，例如无卷曲或无差异，从而启用一种灵活的方法来近似物理过程。提出了参数统计模型，以模拟单位球和球形壳上的随机向量场。这些随机场是用矢量题表示的，并且可以表现出非高斯特征。在此建模范式下提出了一套方法论，以分析和预测在地球物理学中产生的大规模时空标量和矢量过程，例如地球和基于卫星的测量值，对地球的主要磁场或电离层电层电磁场。还研究了与所提出的矢量登陆的结构和特性以及它们所代表的随机矢量场有关的理论问题。通过多分辨率分析对随机场进行建模的灵活框架进一步利用，以通过图形光谱小波在图上构建非高斯过程。该协作项目需要从不同领域（例如多分析分析，空间统计学，光谱图理论，贝叶斯和大规模计算，太空物理学和地球物理学）汇集技能和知识。该奖项反映了NSF的法定任务，并通过基金会的知识优点和广泛的影响来通过评估来通过评估来进行评估。