Long Time Scales and Unlikely Events: Sampling and Coarse Graining Strategies

长时间尺度和不太可能发生的事件：采样和粗粒度策略

• 批准号: 1109731
• 负责人: Jonathan Weare
• 金额: $ 17.5万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1109731&HistoricalAwards=false
• 关键词: Long; Time; Scales; Unlikely; Events

WeareDMS-1109731 The investigator uses tools from probability theory, partial differential equations, and numerical analysis to analyze and simulate interesting physical phenomena that occur on very long time scales or are very unlikely to be observed. Such problems arise in nearly all areas of science and often involve stochastic effects. The investigation of any stochastic system ultimately reduces to the sampling of some random variable. Most sampling applications are limited by the presence of strong spatial correlations and unlikely or long time scale events. Overcoming these obstacles is the key to understanding many of the most important scientific mysteries such as protein folding and climate change, and will be the subject of increased intellectual effort in the near future. This project results in several new methods for attacking problems of this kind as well as applications of these techniques to important problems in engineering, geophysics, and chemistry. In particular the investigator develops and applies new affine invariant ensemble sampling schemes that are relatively insensitive to spatial correlations. These samplers are applied to various statistical inverse problems. The investigator also mathematically studies the convergence of these samplers. The investigator applies new highly efficient importance sampling techniques for rare events to applications in geophysical data assimilation. For long time scale events such as chemical reactions the investigator introduces a new branching process that focuses computational effort on reactive trajectories as well as new parallel-in-time techniques to better utilize today's massively parallel supercomputers on problems involving electronic structure calculations. Finally the investigator rigorously establishes connections between various fine scale models of crystal relaxation and continuum descriptions. Continuum descriptions offer the possibility of reaching much longer time scales computational by removing strongly correlated degrees of freedom. The investigator develops new techniques for studying phenomena that occur over long time scales or involve rare events. The techniques are applied to important problems such as exoplanet discovery, the prediction of rare transitions of the Kuroshio current running along the eastern coast of Japan, crystal surface growth, and several challenging chemical and bio-chemical problems. In general, techniques capable of reaching long time scales and simulating rare events have the potential to significantly impact many problems crucial to our national interests, e.g. drug design, global warming, hazard prediction for CO2 and nuclear waste storage, prediction of extreme geological events like earth quakes and volcanic eruptions, prediction of extreme weather events like hurricanes, prediction of extreme climate events like draughts, drug validation, deep time analysis (analysis of the geologic record), discovery of extra terrestrial life and life in extreme environments, and disease propagation. Even with the massive computing power currently available these problems are not expected to be solved by conventional "brute force" techniques any time soon. Techniques designed to directly interrogate the phenomena of interest and to make more efficient use of large-scale computing power are required. The development and analysis of these techniques form the core of this project.

WeareDMS-1109731 研究人员使用概率论、偏微分方程和数值分析中的工具来分析和模拟在很长的时间尺度上发生或不太可能被观察到的有趣的物理现象。 此类问题几乎出现在所有科学领域，并且通常涉及随机效应。 对任何随机系统的研究最终都会归结为对某些随机变量的采样。 大多数采样应用都受到强空间相关性和不太可能发生或长时间尺度事件的限制。 克服这些障碍是理解许多最重要的科学谜团（例如蛋白质折叠和气候变化）的关键，并且将成为在不久的将来增加智力努力的主题。 该项目产生了几种解决此类问题的新方法，并将这些技术应用于工程、地球物理和化学中的重要问题。 特别是，研究者开发并应用了新的仿射不变集合采样方案，该方案对空间相关性相对不敏感。 这些采样器适用于各种统计逆问题。 研究人员还对这些采样器的收敛性进行了数学研究。 研究人员将罕见事件的新型高效重要性采样技术应用于地球物理数据同化中。 对于化学反应等长时间尺度的事件，研究人员引入了一种新的分支过程，该过程将计算工作集中在反应轨迹上，以及新的并行时间技术，以更好地利用当今的大规模并行超级计算机来解决涉及电子结构计算的问题。 最后，研究人员严格建立了晶体弛豫的各种精细尺度模型和连续统描述之间的联系。 连续体描述通过消除强相关的自由度，提供了达到更长的时间尺度计算的可能性。 研究人员开发新技术来研究长期发生的现象或涉及罕见事件的现象。 这些技术应用于解决系外行星发现、日本东海岸黑潮罕见转变的预测、晶体表面生长以及一些具有挑战性的化学和生物化学问题等重要问题。 一般来说，能够达到长时间尺度并模拟罕见事件的技术有可能对许多对我们国家利益至关重要的问题产生重大影响，例如药物设计、全球变暖、二氧化碳和核废料储存的危险预测、地震和火山爆发等极端地质事件预测、飓风等极端天气事件预测、干旱等极端气候事件预测、药物验证、深度时间分析（地质记录分析）、外星生命和极端环境中生命的发现以及疾病传播。 即使目前拥有强大的计算能力，这些问题预计也不会很快通过传统的“强力”技术得到解决。 需要旨在直接询问感兴趣的现象并更有效地利用大规模计算能力的技术。 这些技术的开发和分析构成了该项目的核心。