Collaborative Proposal: Density-enhanced data assimilation for hyperbolic balance laws

合作提案：双曲平衡定律的密度增强数据同化

• 批准号: 1620278
• 负责人: Ilya Timofeyev
• 金额: $ 19万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-01 至 2020-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620278&HistoricalAwards=false
• 关键词: Collaborative; Proposal; Density; enhanced; data; Collaborative; Proposal; Density; enhanced; data

The research addresses the urgent need to develop efficient computational tools to process the dramatically increasing amounts of observational data. Management of many complex systems (e.g., traffic) has to confront the uncertainty in both their current and future state. This uncertainty typically increases with time, leading to less accurate and useful predictions. Thus, it is important to develop practical methods for "adjusting" the probabilistic state of the system and reducing uncertainty using observational data. This approach is broadly referred to as data assimilation. We will develop novel techniques for incorporating observational data to reduce uncertainty in predictions in two particular areas of national interest: fluid dynamics (e.g., flood forecasting) and traffic management. Both are of vital importance to sustainable development of our society.We propose to develop a novel data assimilation framework for physical processes whose time-dynamics is described by hyperbolic conservation laws. This framework takes advantage of a kinetic representation of hyperbolic systems and, thus, availability of explicit deterministic equations for the time evolution of probability density function for dependent variables. These equations can often be derived and solved exactly, yielding explicit analytical solutions for the marginal and joint probability density functions. For systems of hyperbolic conservation laws an appropriate closure assumption is needed. Thus, the proposed framework relies on the kinetic representation, which takes the form of linear equations for joint probability density functions. Bayesian updating is utilized to incorporate observations into the prediction.

该研究解决了开发有效的计算工具的迫切需求，以处理大量观察数据的数量。许多复杂系统（例如流量）的管理必须面对当前和未来状态的不确定性。这种不确定性通常会随着时间而增加，从而导致准确和有用的预测。因此，开发“调整”系统概率状态并使用观察数据降低不确定性的实用方法很重要。这种方法通常称为数据同化。我们将开发新的技术，用于合并观察数据，以减少国家感兴趣的两个特定领域的预测中的不确定性：流体动态（例如洪水预测）和交通管理。两者对于我们社会的可持续发展都至关重要。我们建议为物理过程开发一种新颖的数据同化框架，其时间动力学由双曲线保护法描述。该框架利用双曲线系统的动力学表示，因此，对于因变量而言，对于概率密度函数的时间演变而言，明确确定性方程的可用性。这些方程通常可以准确地得出和求解，从而为边际和关节概率密度函数提供明确的分析解决方案。对于双曲线保护法系统，需要适当的封闭假设。因此，所提出的框架依赖于动力学表示，该动力学表示以接头概率密度函数为线性方程式。贝叶斯更新用于将观测值纳入预测中。