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国际高等研究学院（https://indico.sissa.it/event/8/）举行。美国国家科学基金会的这项奖励专门支持美国青年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，并讨论算法和数学研究的未来方向，以量化复杂系统的输出中的不确定性，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，研讨会将影响科学、工程、社会、金融、经济、环境和商业环境。工作坊的结构旨在最大限度地发挥其短期和长期影响。研讨会的科学重点是三个非常有前途的算法领域，这些领域的近期改进将对上述所有设置产生直接和持久的影响。研讨会的一个重要特点是几个讨论环节，参与者可以使用从讲座中收集的信息来就每个算法领域的最佳研究方向达成一致。为了最大限度地发挥其影响，将通过一个网站和在专业协会新闻杂志上发表文章来广泛传播讨论的结果。最后，由于绝大多数与会者是初级研究人员，讲习班的长期影响将大大增强。研讨会的讲座和讨论将极大地帮助那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和不确定性的概率描述建模的复杂系统。在保持不确定性量化所需保真度的同时降低成本可以通过两种方式实现：一种可以减少获得偏微分方程近似解的成本，或者可以减少必须求解偏微分方程的次数。对于前者，讲习班将侧重于两种方法。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。第二个是改进的降阶模型的发展，它使偏微分方程的离散化更小，求解成本也更低。减少求解偏微分方程的次数将通过改进逼近解对随机参数的依赖的方法来解决，特别是当涉及大量参数时。高维近似理论的最新进展将发挥突出作用。

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.