Workshop on Quantification of Uncertainty: Improving Efficiency and Technology

不确定性量化研讨会：提高效率和技术

• 批准号: 1707658
• 负责人: Max Gunzburger
• 金额: $ 2.02万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-03-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1707658&HistoricalAwards=false
• 关键词: Workshop; Quantification; Uncertainty; Improving; Efficiency

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.

“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级研究学院举行，https://indico.sissa.it/event/8/。该 NSF 奖项专门支持美国初级参加者参加研讨会的费用，他们将受益于与领先专家的交流。国际知名专家将介绍复杂系统输出不确定性量化方面的最新进展，并讨论算法和数学研究的未来方向，这些复杂系统受输入中的随机不确定性影响。由于此类系统无处不在，研讨会将影响科学、工程、社会、金融、经济、环境和商业环境。研讨会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举行多次讨论会，参与者可以利用从讲座中收集的信息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影响力，讨论结果将通过网站和在专业协会新闻杂志上发表文章的方式广泛传播。最后，由于绝大多数参与者都是初级研究人员，研讨会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参与者形成前沿的长期研究计划。研讨会将讨论通过偏微分方程和不确定性的概率描述建模的复杂系统。可以通过两种方式实现在保持该设置的不确定性量化的期望保真度的同时降低成本：一种可以降低获得偏微分方程的近似解的成本和/或可以减少偏微分方程的次数必须解决。对于前者，研讨会将重点关注两种方法。首先是为由有限元离散化等产生的大型离散系统开发更高效的求解器。第二个是改进的降阶模型的开发，其结果是偏微分方程的离散化更小，因此求解起来更便宜。通过开发用于近似解对随机参数的依赖性的改进方法，特别是当涉及大量参数时，可以解决偏微分方程求解次数的减少问题。高维近似理论的最新进展将发挥重要作用。