Workshop on Functional Analytic Methods in Error Prediction with Applications

误差预测中的泛函分析方法及其应用研讨会

• 批准号: 1565738
• 负责人: Victor Ginting
• 金额: $ 2.98万
• 依托单位: University of Wyoming
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-05-01 至 2017-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1565738&HistoricalAwards=false
• 关键词: Workshop; Functional; Analytic; Methods; Error

This project provides travel and subsistence support for participants in the workshop "Functional Analytic Methods in Error Prediction with Applications" held at the University of Wyoming on June 13-17, 2016. The workshop is part of an annual activity spearheaded by the Rocky Mountain Mathematics Consortium (RMMC). The workshop is aimed at exposing graduate students and junior researchers to recent progress in computational sciences, particularly in error estimation techniques utilized in a class of multi-physics and multi-scale problems inheriting various levels of uncertainty. The workshop is designed to be strongly interdisciplinary. Workshop presentations and lectures are a blend of colloquium type and more in-depth style, with the intention of allowing junior participants to gain knowledge that are potentially useful in their future endeavors, and at the same time giving more experienced participants ample opportunity to initiate research collaboration.Any numerical approximation/simulation for solving mathematical problems contains some errors. These errors are often functionally dependent on some parameters associated with the method. Formally, a robust numerical method should exhibit a behavior in which the errors vanish in the limiting process associated with the parameters. A standard practice is to estimate the errors in terms of the parameters and some regularity assumptions of the original problems. Unfortunately, many applications prevent imposing those theoretical assumptions, thereby creating a need to monitor the errors in real time simulation. Having this availability will enhance the robustness of the approximation in the predictive simulation. Furthermore, a closely related aspect to error estimation is quantifying the uncertainty that can be present both in the original problem and in the techniques employed to approximate it. The appropriate strategy to tackle this is multifaceted, involving reliance on sophisticated mathematical and statistical tools. This workshop provides a forum for researchers to address all these issues. More information can be found at the workshop website: www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/

该项目为2016年6月13日至17日在怀俄明大学举办的《误差预测中的泛函分析方法及其应用》研讨会的参与者提供差旅和生活支持。该研讨会是落基山数学联合会(RMMC)带头开展的年度活动的一部分。讲习班的目的是让研究生和初级研究人员了解计算科学的最新进展，特别是在一类继承了不同程度不确定性的多物理和多尺度问题中使用的误差估计技术。该研讨会被设计为具有很强的跨学科性质。工作坊的演讲和讲座是一种学术讨论会和更深入的风格相结合的形式，目的是让初级参与者获得对他们未来的努力可能有用的知识，同时给更有经验的参与者提供充分的机会来启动研究合作。任何用于解决数学问题的数值近似/模拟都包含一些错误。这些错误通常在功能上取决于与该方法相关的一些参数。形式上，稳健的数值方法应该表现出这样一种行为，即在与参数相关的极限过程中误差消失。一种标准的做法是根据原始问题的参数和一些正则性假设来估计误差。不幸的是，许多应用程序阻止强加这些理论假设，从而产生了在实时模拟中监控误差的需求。具有这种可用性将增强预测模拟中近似的稳健性。此外，与误差估计密切相关的一个方面是量化原始问题和近似该问题所采用的技术中可能存在的不确定性。解决这一问题的适当战略是多方面的，包括依赖复杂的数学和统计工具。这个研讨会为研究人员提供了一个论坛来解决所有这些问题。欲了解更多信息，请访问研讨会网站：www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/