Workshop on Stochastic Multiscale Methods: Mathematical Analysis and Algorithms; August 2009, Los Angeles, CA

随机多尺度方法研讨会：数学分析和算法；

• 批准号: 0917661
• 负责人: Roger Ghanem
• 金额: $ 2.49万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-15 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0917661&HistoricalAwards=false
• 关键词: Workshop; Stochastic; Multiscale; Methods; Mathematical

Exchanging information across scales is one of the most significant challenges in multiscale modeling and simulation. By necessity, and naturally within a multiscale context, information is truncated as it is presented to a coarser scale, and is enriched as it traverses the opposite path. Information is lost and corrupted as it is, respectively, upscaled and downscaled. Mitigating these errors can be set on rigorous ground through a probabilistic description of information, whence finite-dimensional approximations of measures provides an analytical path for describing the coarsening and refining of information. Stochastic analysis, therefore, provides a rational context for the analysis of multiscale methods. This workshop on "Stochastic Multiscale Methods: Mathematical Analysis and Algorithms"will serve to define challenges and opportunities in the development of stochastic multiscale methods for various problems in science and engineering. Issues of uncertainty quantification, model validation, and optimization under uncertainty have taken center stage in many areas of science and engineering. Likewise, multiscale modeling and computing capabilities are becoming the standard against which model-based predictions are gauged. It thus behooves the scientific community, at this juncture, to elucidate the mathematical foundation of stochastic multiscale concepts so as to ensure a steady evolution of scientific capabilities as engines of economical growth societal well-being. This workshop will initiate a dialog between mathematicians, mechanicians, and computational scientists that will lay the foundation for an accelerated growth in stochastic multiscale methods.Rapid growth in computational resources has heightened the expectation that scientific knowledge can indeed be a driver for societal well-being and betterment. At the same time, our ability to measure the natural and social world around has significantly increased, aided by technological development in sensors, the internet, and other modalities of communication. Science is thus faced, simultaneously, with a complex description of reality at an unprecendented resolution, and the possibility to describe this reality with mathematical models of increasing complexity.Multiscale descriptions of physical problems can be viewed as attempts to take advantage of these new oppotunities, while tackling the conceptual challenges they inevitably present.The communities of stochastic analysis and computational science have evolved essentially along separate paths. The path forward, however, in the direction of disruptive scientific impact, requires significant exchange andcollaboration. It is the intent of this Workshop ``Stochastic Multiscale Methods:Mathematical Analysis and Algorithms'' to bring together leading researchers in these two fields with view to delineate new horizons and forge new synergies that will accelerate the evolution of multiscale capabilities to become an enabler of scientific and economic progress.

跨量表交换信息是多尺度建模和仿真中最重要的挑战之一。 必要时，自然而然地，在多尺度的环境中，信息被截断了，因为它被呈现为更粗糙的尺度，并且随着遍历相反的路径而富集。信息分别丢失和腐败，分别是高扫描和缩小的。 通过对信息的概率描述，可以在严格的基础上设置这些误差，措施的有限维近似值为描述信息的粗化和精炼提供了一个分析路径。因此，随机分析为分析多尺度方法提供了合理的背景。 这个关于“随机多尺度方法：数学分析和算法”的研讨会将有助于在开发科学和工程中各种问题的随机多尺度方法中定义挑战和机遇。 在不确定性下，不确定性量化，模型验证和优化的问题在许多科学和工程领域都占据了中心地位。 同样，多尺度建模和计算功能已成为测量基于模型的预测的标准。 因此，在这个关头，它应该理解科学界，以阐明随机多尺度概念的数学基础，以确保科学能力的稳定发展，因为经济增长社会健康的发动机。 该研讨会将启动数学家，技工和计算科学家之间的对话，这将为随机多尺寸方法的加速增长奠定基础。计算资源的影响增长增强了人们的期望，即科学知识确实可以成为社会健康和改善的驱动力。 同时，通过传感器，互联网和其他交流方式的技术发展，我们衡量自然和社会世界的能力已大大提高。 因此，科学是同时面对的，并以未固定的解决方案对现实进行了复杂的描述，并且有可能通过数学模型的数学模型来描述这种现实。对物理问题的数学描述可以看作是试图利用这些新的反对派的尝试，同时又可以解决这些概念性的挑战，而这些概念性既定不可能地均可置于现实状态。然而，朝着破坏性科学影响的方向前进，需要大量的交换和策略。 这是该研讨会的目的``随机多尺度方法：数学分析和算法''，将这两个领域的主要研究人员汇集在一起​​，以划定新的视野并造就新的协同作用，以加速多阶段能力的进化，以成为科学和经济进步的能力。