DMS-EPSRC Collaborative Research: Sharp Large Deviation Estimates of Fluctuations in Stochastic Hydrodynamic Systems

DMS-EPSRC 合作研究：随机水动力系统波动的急剧大偏差估计

• 批准号: 2012510
• 负责人: Eric Vanden-Eijnden
• 金额: $ 22.85万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-08-15 至 2023-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012510&HistoricalAwards=false
• 关键词: DMS; EPSRC; Collaborative; Research; Sharp

Extreme events can be highly impactful. They are typically rare, which is fortunate if their consequences are negative on society, but also makes them difficult to predict. The focus of this project is to develop computational tools that can be applied to gain understanding of how extreme events occur in complex stochastic systems. Examples are models for the forecasting of extreme weather-related events like tropical storms and flooding as well as the spread of pollutants in case of ocean oil spills. These tools will enable researchers to ask questions beyond what is currently possible. This will lead to transformative improvement of current predictive models, which is essential for efficient management of natural and man-made disasters. Further applications include the characterization of extreme events in stochastic models that behave similar to fluids, for example in the context of epidemics, traffic, and star formation. This collaborative project will support one graduate student per year at NYU.Rare events are difficult to observe in controlled (numerical or physical) experiments, even for low-dimensional systems. The difficulty increases with the number of degrees of freedom, which makes high-dimensional systems even harder to analyze — fluids described by stochastic hydrodynamic models are a particular example of interest. As a result the questions that researchers can ask in order to gain insights about extreme events in these systems are often limited. The goal of this project is to analyze rare but important events in complex systems by developing new mathematical and computational tools to establish their most likely way of occurrence and calculate sharp asymptotic estimates (with prefactor included) of their probability and recurrence time. The aim is to create a toolbox applicable to a wide range of models with a large number of degrees of freedom described by stochastic partial differential equations (PDEs), like advection-diffusion equations and Navier-Stokes equations, and transferable across disciplinary borders. These tools will be applied to stochastic hydrodynamic systems in order to gain deeper insights of classical turbulence. In addition, the efficiency of this novel approach will be demonstrated in the context of real-world applications, in particular the advection of pollutants and the capsizing of ships.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.

极端事件的影响通常非常罕见，如果它们的后果对社会产生负面影响，那是幸运的，但也使它们难以预测，该项目的重点是开发可用于了解其影响的计算工具。极端事件发生在复杂的随机系统中。例如，预测热带风暴和洪水等极端天气相关事件的模型，以及海洋石油泄漏情况下污染物扩散的模型，这些工具将使研究人员能够提出超出实际情况的问题。目前这将带来变革。改进当前的预测模型，这对于有效管理自然和人为灾害至关重要，进一步的应用包括在表现类似于流体的随机模型中表征极端事件，例如在流行病、交通和恒星形成的背景下。该合作项目每年将支持纽约大学一名研究生。在受控（数值或物理）实验中很难观察到罕见事件，即使对于低维系统也是如此。随着自由度的增加，观察难度也会增加。维度系统更难分析——随机流体动力学模型描述的流体是一个特别令人感兴趣的例子，因此，研究人员为了深入了解这些系统中的极端事件而提出的问题通常是有限的。通过新的数学和计算工具开发复杂系统，以确定其最可能的发生方式并计算其概率和重现时间的锐渐近估计（包括前因数），其目的是创建一个适用于各种模型的工具箱。大量自由度描述为随机偏微分方程（PDE），如平流扩散方程和纳维-斯托克斯方程，并且可以跨学科边界转移，这些工具将应用于随机流体动力学系统，以获得对经典湍流的更深入的了解。这种新颖的方法将在现实世界的应用中得到证明，特别是反映污染物的平流和船舶的倾覆。该奖项符合 NSF 的法定使命，并已被视为值得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来支持。