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Analysis and Simulation of Extremes and Rare Events in Complex Systems

复杂系统中极值和罕见事件的分析与仿真

基本信息

批准号：
2009923
负责人：
Matthew Nicol
金额：
$ 36.87万
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：
2020
资助国家：
美国
起止时间：
2020-07-15 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2009923&HistoricalAwards=false
关键词：
Analysis Simulation Extremes Rare Events

项目摘要

It is vital to be able to accurately predict the probability of rare and extreme events, such as heatwaves and hurricanes, in particular from climate models and climate data. Better techniques to estimate the probability of rare events and extremes are of obvious benefit to society, and will lead to better planning for floods, heatwaves, and other exigencies. Prediction from computer simulations or from real world data is an extremely challenging task. Brute force simulations by computer are often not feasible; the number of computer simulations it requires to obtain accurate estimates of the probability and form of rare events is too high for this to be a useful method in practice. In addition to this, we typically lack sufficient data to make confident predictions about rare events and extremes from climate records. Two strands of research will be developed. First, to develop a rigorous understanding of a technique from probability called importance sampling in simple mathematical models with the aim to have a firm foundation for their implementation in more realistic and complicated climate models. Importance sampling in a sense makes rare events less rare and allows reliable estimates of rare events in situations where brute force simulations are not feasible. Second, a statistical technique called extreme value theory will be developed in order to allow better estimates of the probabilities of the duration of extremes, such as heatwaves, from climate models and data.The Principal Investigators will develop a technique from importance sampling called genealogical particle analysis to speed up sampling by making rare events more common. The steps enabling the speedup may be tracked and accounted for to obtain more accurate estimates of rare events with less computational effort. Extreme value theory for physical observables such as temperature, wind velocity and energy for climate models will be developed and tested on simple climate models and extended to determine the probability of the duration of extremes, such as heatwaves, from time series data. Clustering algorithms based on information theory will be developed to sort data from spatially distinct sites to amplify the data available to better predict, for example, heatwaves and cold spells. The investigation will be in part theoretical, numerical and data analytic. Progress in this area would significantly improve our conceptual understanding of rare events and extremes in complex systems such as the climate and our ability to predict their behavior. The investigators past work on extreme value theory has been recognized and cited by meteorologists; it has detailed how extreme value theory should be applied to deterministic models. The current research will be at the interface of applications and of general interest to scientists modeling complex systems. In addition, the project will provide excellent training in probabilistic techniques and data analysis for the graduate students involved in the research.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.

能够准确预测热浪和飓风等罕见和极端事件的概率至关重要，特别是从气候模型和气候数据。更好地估计罕见事件和极端事件的概率的技术对社会有明显的好处，并将导致更好地规划洪水、热浪和其他紧急情况。从计算机模拟或从真实世界数据进行预测是一项极具挑战性的任务。用计算机进行暴力模拟通常是不可行的；为了获得对罕见事件的概率和形式的准确估计，它需要进行计算机模拟的次数太多，这在实践中不是一种有用的方法。除此之外，我们通常缺乏足够的数据，无法根据气候记录对罕见事件和极端事件做出自信的预测。将开展两个方面的研究。首先，在简单的数学模型中发展一种被称为重要性抽样的概率技术的严格理解，目的是为它们在更现实和复杂的气候模型中的实施奠定坚实的基础。在某种意义上，重要性抽样使罕见事件变得不那么罕见，并允许在暴力模拟不可行的情况下可靠地估计罕见事件。其次，将开发一种名为极值理论的统计技术，以便从气候模型和数据中更好地估计极端事件(如热浪)持续时间的概率。首席研究人员将开发一种称为系谱粒子分析的重要抽样技术，通过使罕见事件变得更加常见来加快抽样速度。实现加速的步骤可以被跟踪和考虑，以便以更少的计算工作量获得对罕见事件的更准确的估计。气候模型的温度、风速和能量等物理观测的极值理论将在简单的气候模型上进行开发和测试，并扩展到从时间序列数据确定极端事件(如热浪)持续时间的概率。将开发基于信息论的聚类算法，对来自不同空间位置的数据进行分类，以放大可用于更好地预测例如热浪和寒流的数据。调查将在一定程度上进行理论、数值和数据分析。这一领域的进展将显著提高我们对气候等复杂系统中罕见事件和极端事件的概念性理解，以及我们预测它们行为的能力。研究人员过去在极值理论方面的工作得到了气象学家的认可和引用；它详细说明了极值理论应该如何应用于确定性模式。目前的研究将在应用程序的界面上进行，并引起对复杂系统建模的科学家的普遍兴趣。此外，该项目将为参与研究的研究生提供概率技术和数据分析方面的优秀培训。该奖项反映了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。