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: 2012548
• 负责人: Tobias Schaefer
• 金额: $ 14.76万
• 依托单位: CUNY College of Staten Island
• 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 2024-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2012548&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.

极端事件可能具有很高的影响力。它们通常很少见，如果他们的后果对社会负面影响，这很幸运，但也使它们难以预测。该项目的重点是开发可应用的计算工具，以了解复杂随机系统中极端事件的发生方式。例子是预测与热带风暴和洪水等极端天气相关事件的模型，以及在海洋溢油时污染物的传播。这些工具将使研究人员能够提出以外的问题。这将导致当前预测模型的变革性改善，这对于有效地管理自然和人为灾难至关重要。进一步的应用包括在随机模型中表征与流体相似的随机模型中的表征，例如在流行病，流量和恒星形成的背景下。这个协作项目将每年在纽约大学举行的一名研究生。在受控（数值或物理）实验中，即使对于低维系统，也很难观察到Rare事件。随着自由度的数量，困难的增加，这使得高维系统甚至更难分析 - 由随机流体动力学模型描述的流体是感兴趣的一个例子。结果，研究人员可以提出的问题以获取有关这些系统中极端事件的见解通常受到限制。该项目的目的是通过开发新的数学和计算工具来分析复杂系统中的罕见但重要事件，以确定其最可能的发生方式，并计算出其概率和复发时间的尖锐不对称估计（包括预先因素）。目的是创建一个适用于各种模型的工具箱，其随机部分微分方程（PDES）描述了许多自由度，例如广告扩散方程和Navier-Stokes方程，并且可在纪律界面上转移。这些工具将应用于随机流体动力学系统，以获得更深入的经典湍流见解。此外，这种新颖方法的效率将在现实世界应用的背景下，尤其是污染物的广告和船舶的倾斜。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛的审查标准通过评估来通过评估来支持的。