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Collaborative Research: Construction and Analysis of Numerical Methods for Stochastic Inverse Problems with Application to Coastal Hydrodynamics

合作研究：随机反问题数值方法的构建和分析及其在海岸流体动力学中的应用

基本信息

批准号：
1818847
负责人：
Clinton Dawson
金额：
$ 10万
依托单位：
University of Texas at Austin
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：
2018-08-01 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818847&HistoricalAwards=false
关键词：
Collaborative Research Construction Analysis Numerical

项目摘要

As observed in past hurricanes such as Katrina (2005), Ike (2008), Sandy (2012), and the sequence of hurricanes over the 2017 season, flooding due to storm surge and rainfall causes tremendous damage to coastal communities. Preparing for future hurricane impacts requires the ability to predict characteristics of inland flooding due to surge, most importantly water levels, currents, and extent of inundation. Accurate predictions of surge require determining critical inputs to models related to the physical characteristics of coastal regions that are expensive to obtain and evolve in time. This research project focuses on quantifying and reducing uncertainties in these critical inputs using novel mathematical techniques to both extract information from existing data and aid in the design of future data collection efforts.More specifically, this project focuses on the construction, analysis, and implementation of numerical methods for a stochastic inverse problem defined by the melding of observational data and high-fidelity mathematical models to perform scientific and engineering inference and prediction for complex physical systems. This research applies broadly to complex, time-evolving physical systems depending on high dimensional parameter spaces. Mathematical areas utilized in this research include computational measure theory, differential geometry, functional analysis, probability theory, and numerical analysis. Dissemination of results to the broader scientific community will be accomplished in part by the development and implementation of computational algorithms in public domain code that are applied to a state-of-the-art storm surge model.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.

正如卡特里娜飓风（2005 年）、艾克飓风（2008 年）、桑迪飓风（2012 年）以及 2017 年飓风季的一系列飓风所观察到的那样，风暴潮和降雨造成的洪水对沿海社区造成了巨大破坏。为未来的飓风影响做好准备需要能够预测潮汐造成的内陆洪水特征，最重要的是水位、水流和淹没程度。准确预测潮汐需要确定与沿海地区物理特征相关的模型的关键输入，而这些输入和及时发展的成本很高。该研究项目的重点是使用新颖的数学技术来量化和减少这些关键输入中的不确定性，以从现有数据中提取信息并帮助设计未来的数据收集工作。更具体地说，该项目的重点是构建、分析和实施随机反问题的数值方法，该问题通过观测数据和高保真数学模型的融合来定义，以对复杂物理进行科学和工程推理和预测。系统。这项研究广泛适用于依赖高维参数空间的复杂、随时间演化的物理系统。本研究中使用的数学领域包括计算测量理论、微分几何、泛函分析、概率论和数值分析。将结果传播到更广泛的科学界将部分通过在公共领域代码中开发和实施计算算法来完成，这些算法应用于最先进的风暴潮模型。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。