Analysis and Simulation of Extremes and Rare Events in Complex Systems

能够准确预测罕见和极端事件（如热浪和飓风）的概率至关重要，特别是要利用气候模式和气候数据。更好的技术来估计罕见事件和极端事件的概率显然对社会有益，并将导致更好地规划洪水、热浪和其他紧急情况。从计算机模拟或现实世界的数据进行预测是一项极具挑战性的任务。用计算机进行蛮力模拟通常是不可行的；为了准确估计罕见事件的概率和形式，需要进行大量的计算机模拟，因此这种方法在实践中不太有用。除此之外，我们通常缺乏足够的数据，无法从气候记录中对罕见事件和极端事件做出自信的预测。将开展两方面的研究。首先，在简单的数学模型中对一种称为重要性抽样的概率技术有一个严格的理解，目的是为在更现实和复杂的气候模型中实施这些模型打下坚实的基础。重要性抽样在某种意义上使罕见事件不那么罕见，并允许在暴力模拟不可行的情况下对罕见事件进行可靠的估计。其次，将发展一种称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。首席研究人员将从重要采样中开发一种称为系谱粒子分析的技术，通过使罕见事件更常见来加快采样速度。可以跟踪和解释启用加速的步骤，以便以更少的计算工作量获得对罕见事件的更准确估计。将开发用于气候模型的物理可观测值（如温度、风速和能量）的极值理论，并在简单气候模型上进行测试，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。将开发基于信息理论的聚类算法，对空间上不同的地点的数据进行分类，以扩大可用的数据，以便更好地预测，例如，热浪和寒潮。调查将包括理论、数值和数据分析。这一领域的进展将大大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，以及我们预测其行为的能力。研究者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型。目前的研究将在应用界面和普遍感兴趣的科学家建模复杂系统。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。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.