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.

极端事件可能会产生很大的影响。它们通常是罕见的，这是幸运的，如果它们的后果对社会是负面的，但也使它们难以预测。这个项目的重点是开发计算工具，这些工具可以用来了解极端事件如何在复杂的随机系统中发生。例如，预报热带风暴和洪水等与极端天气有关的事件的模型，以及在发生海洋石油泄漏时污染物的扩散。这些工具将使研究人员能够提出超出目前可能的问题。这将导致对当前预测模型的变革性改进，这对有效管理自然灾害和人为灾害至关重要。进一步的应用包括描述随机模型中的极端事件，这些模型的行为类似于流体，例如在流行病、交通和恒星形成的背景下。这个合作项目将支持纽约大学每年一名研究生。罕见的事件在受控(数值或物理)实验中很难观察到，即使是低维系统也是如此。难度随着自由度的增加而增加，这使得高维系统更难分析--由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往往是有限的。这个项目的目标是通过开发新的数学和计算工具来分析复杂系统中罕见但重要的事件，以确定它们最可能发生的方式，并计算它们的概率和重现时间的精确渐近估计(包括预因子)。其目的是创建一个工具箱，适用于由随机偏微分方程组(PDE)描述的具有大量自由度的广泛模型，如对流扩散方程和Navier-Stokes方程，并可跨学科边界转移。这些工具将应用于随机水动力系统，以获得对经典湍流的更深层次的了解。此外，这种新方法的效率将在实际应用中得到证明，特别是污染物的平流和船舶的倾覆。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。