Workshop on Functional Analytic Methods in Error Prediction with Applications

该项目为2016年6月13日至17日在怀俄明大学举行的“误差预测中的功能分析方法与应用”研讨会的参与者提供旅行和生活支持。该研讨会是由落基山数学联盟（RMMC）牵头的年度活动的一部分。研讨会旨在让研究生和初级研究人员了解计算科学的最新进展，特别是在继承不同程度不确定性的多物理场和多尺度问题中使用的误差估计技术。该研讨会的设计是跨学科的。研讨会的演讲和讲座是讨论会类型和更深入的风格的混合，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，同时为更有经验的参与者提供充分的机会来发起研究合作。任何用于解决数学问题的数值近似/模拟都存在一些误差。这些错误通常在功能上依赖于与方法相关的一些参数。形式上，鲁棒数值方法应表现出误差在与参数相关的极限过程中消失的行为。一种标准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，因此需要在实时模拟中监视误差。具有这种可用性将增强预测仿真中近似的鲁棒性。此外，与误差估计密切相关的一个方面是量化不确定性，这种不确定性既存在于原始问题中，也存在于用来近似它的技术中。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。本次研讨会为研究人员提供了一个讨论所有这些问题的论坛。更多信息请访问研讨会网站：www.uwyo.edu/math/additional-learning-opportunities/rmmc-summer-school/

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/