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

• 批准号: 1818777
• 负责人: Donald Estep
• 金额: $ 8.1万
• 依托单位: Colorado State University
• 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 2021-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1818777&HistoricalAwards=false
• 关键词: Collaborative; Research; Construction; Analysis; Numerical

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.

正如过去的飓风如卡特里娜（2005年），艾克（2008年），桑迪（2012年）以及2017年飓风季的飓风序列所观察到的那样，风暴潮和降雨造成的洪水对沿海社区造成了巨大的破坏。为未来的飓风影响做准备需要有能力预测由浪涌引起的内陆洪水的特征，最重要的是水位，水流和淹没范围。准确预测涌浪需要确定与沿海地区物理特性有关的模型的关键输入，而这些输入的获取和演变成本很高。该研究项目的重点是量化和减少这些关键输入的不确定性，使用新的数学技术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，该项目侧重于构建，分析，和实现的数值方法的随机反问题所定义的融合的观测数据和高-保真度数学模型，用于对复杂的物理系统进行科学和工程推断和预测。这项研究广泛适用于依赖于高维参数空间的复杂的，随时间演化的物理系统。在这项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开发和实施公共领域代码的计算算法来实现，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知识价值和更广泛的影响审查标准进行评估，被认为值得支持。