Workshop on Quantification of Uncertainty: Improving Efficiency and Technology

《不确定性的量化：提高效率和技术》研讨会将于2017年7月18日至21日在意大利的里雅斯特的国际高级研究学院举行，网址：https://indico.sissa.it/event/8/.这一NSF奖项专门资助美国初级与会者参加研讨会的费用，他们将从与领先专家的接触中受益。国际公认的专家将介绍最近的进展，并讨论在量化复杂系统输出中的不确定性方面的算法和数学研究的未来方向，这些系统的输入受到随机不确定性的影响。由于这样的系统无处不在，研讨会将对科学、工程、社会、金融、经济、环境和商业环境产生影响。讲习班的结构设计是为了最大限度地发挥其短期和长期影响。讲习班的科学重点是三个非常有希望的算法领域，近期的改进将对上述所有环境产生直接和持久的影响。研讨会的一个重要特点是几次讨论，参与者可以在讨论中使用从讲座中收集的信息，就每个算法领域可能的最佳研究方向达成一致。为最大限度地扩大影响，讨论结果将通过一个网站和在专业社会新闻杂志上发表文章的方式广泛传播。最后，讲习班的长期影响将大大增强，因为绝大多数参与者都是初级研究人员。研讨会的讲座和讨论将极大地帮助这些参与者形成前沿的、长期的研究计划。研讨会将讨论由偏微分方程式和不确定性的概率描述建模的复杂系统。在此设置的不确定性量化保持所需保真度的同时降低成本可以通过两种方式实现：一种可以降低获得偏微分方程解的近似解的成本和/或一种可以减少必须求解偏微分方程的次数。对于前者，研讨会将重点讨论两种方法。首先是为大型离散系统开发更有效的求解器，例如有限元离散化。第二是改进的降阶模型的发展，使得偏微分方程的离散化变得更小，因此求解成本也更低。将通过发展改进的方法来近似解对随机参数的依赖性，特别是在涉及大量参数的情况下，来减少偏微分方程解的次数。高维逼近理论的最新进展将发挥重要作用。

The workshop "Quantification of Uncertainty: Improving Efficiency and Technology" will be held on July 18-21, 2017 at the International School for Advanced Studies in Trieste, Italy, https://indico.sissa.it/event/8/. This NSF award exclusively supports the participation costs of junior US-based attendees at the workshop who will benefit from engaging with leading experts. Internationally recognized experts will present recent progress and discuss future directions of algorithmic and mathematical research in the quantification of uncertainties in the outputs of complex systems that are subject to random uncertainties in their inputs. Because such systems are ubiquitous, the workshop will impact the scientific, engineering, social, financial, economic, environmental, and commercial milieus. The structure of the workshop is designed to maximize its short- and long-term impact. The scientific focus of the workshop is on three very promising algorithmic areas for which near-term improvements would have an immediate and lasting impact on all the settings mentioned above. An important feature of the workshop is several discussion sessions at which participants can use the information gathered from the lectures to agree on the best possible research directions for each algorithmic area. To maximize their impact, the results of the discussions will be widely disseminated via a web site and through the publication of articles in professional society news magazines. Finally, the long-term impact of the workshop will be greatly enhanced by having a substantial majority of the participants be junior researchers. The workshop lectures and discussion sessions will greatly help those participants to form cutting-edge, long-term research programs.The workshop will address complex systems modeled by partial differential equations and probabilistic descriptions of uncertainties. Reductions in the cost while maintaining a desired fidelity for uncertainty quantification for this setting can be realized in two ways: one can reduce the cost of obtaining approximate solutions of the partial differential equation and/or one can reduce the number of times the partial differential equation has to be solved. For the former, the workshop will focus on two approaches. First is the development of more efficient solvers for the large discrete systems that arise from, e.g., finite element discretizations. The second is the development of improved reduced-order models that result in much smaller, and thus much cheaper to solve, discretizations of the partial differential equation. Reductions in the number of times the partial differential equation has to be solved will be addressed through the development of improved methods for approximating the dependence of solutions on the random parameters, especially when a large number of parameters is involved. Recent advances in high-dimensional approximation theory will play a prominent role.