Topological and Rigorous Computational Methods for High Dimensional Dynamics

高维动力学的拓扑和严格计算方法

• 批准号: 1841324
• 负责人: Konstantin Mischaikow
• 金额: $ 1.2万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-02-01 至 2020-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1841324&HistoricalAwards=false
• 关键词: Topological; Rigorous; Computational; Methods; Dimensional

The conference 'Topological and Rigorous Computational Methods for High Dimensional Dynamics' is to be held on April 1 - April 30, 2019in Centre des Recherches Mathematiques (CRM), Canada. The revolution of computational and data driven science is well underway. However, mathematically rigorous frameworks for processing the output of this science is lagging. This is of serious concern since these same computational and data driven techniques are having immediate impacts on the private and social sectors of society. It is essential that within the new generation of mathematicians there are researchers capable of addressing these issues. Through the tutorials, junior researchers will be introduced to rapidly developing concepts, techniques, and computational tools designed to address these challenges. Through the workshop lectures they will be made aware of the latest developments in the field.Of equal importance is that their presence will allow them to interact with leaders in the field, to begin to develop connections with researchers from across the world, and ideally to begin research projects that lay the foundations of new techniques for rigorous understanding of the complex nonlinear systems of interest today and in the future.This project will provide support for junior researchers from the USA to participate in a month long special program at the Centre des Recherches Mathematiques (CRM) entitled Topological and Rigorous Computational Methods for High Dimensional Dynamics. The activities will take place from April 1 - April 30, 2019 and consist of tutorials, workshops, and time for collaboration. The research activities of the CRM program focus on two topics. The first theme is how to effectively and rigorously identify invariant structures in infinite dimensional dynamical systems, for example those generated by partial differential equations. The second theme is how to extract robust information from poorly resolved dynamical systems, for example when only partial or coarse data is available.Conference website: http://www.crm.math.ca/crm50/en/activities/2019-activities/topological-and-rigorous-computational-methods-for-high-dimensional-dynamics/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

“高维动力学的拓扑和严格计算方法”会议将于2019年4月1日至4月30日在加拿大数学研究中心（CRM）举行。计算和数据驱动的科学革命正在进行中。然而，用于处理这一科学成果的严格数学框架却滞后了。 这是一个严重的问题，因为这些同样的计算和数据驱动的技术正在对社会的私营和社会部门产生直接影响。重要的是，在新一代的数学家有研究人员能够解决这些问题。 通过教程，初级研究人员将被介绍到快速发展的概念，技术和计算工具，旨在解决这些挑战。通过研讨会讲座，他们将了解该领域的最新发展。同样重要的是，他们的存在将使他们能够与该领域的领导者互动，开始与来自世界各地的研究人员建立联系，理想情况下，开始研究项目，为今天和未来感兴趣的复杂非线性系统的严格理解奠定新技术的基础。这该项目将为来自美国的初级研究人员提供支持，以参加在数学研究中心（CRM）为期一个月的题为高维动力学的拓扑和严格计算方法的特别计划。 活动将于2019年4月1日至4月30日举行，包括教程，研讨会和合作时间。 CRM项目的研究活动集中在两个主题上。 第一个主题是如何有效和严格地识别无穷维动力系统中的不变结构，例如由偏微分方程产生的那些。第二个主题是如何从分辨率不高的动力系统中提取可靠的信息，例如当只有部分或粗略的数据可用时。会议网站：http://www.crm.math.ca/crm50/en/activities/2019-activities/topological-and-rigorous-computational-methods-for-high-dimensional-dynamics/This奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Identifying Nonlinear Dynamics with High Confidence from Sparse Data

• DOI: 10.1137/23m1560252
• 发表时间: 2024-01-01
• 期刊: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
• 影响因子: 2.1
• 作者: Batko，Bogdan;Gameiro，Marcio;Vieira，Ewerton
• 通讯作者: Vieira，Ewerton