MPS-Ascend: Improved Accuracy and Robustness for Numerical Partial Differential Equations and Nonlinear Optimization

MPS-Ascend：提高数值偏微分方程和非线性优化的准确性和鲁棒性

• 批准号: 2213322
• 负责人: Alan Marquez
• 金额: $ 30万
• 依托单位: Marquez, Alan
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-15 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2213322&HistoricalAwards=false
• 关键词: MPS; Ascend; Improved; Accuracy; Robustness

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). PI Alan Marquez is awarded a National Science Foundation Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowship (NSF MPS-Ascend) to conduct a program of research and activities related to broadening participation by groups underrepresented in STEM. This fellowship to Dr. Marquez supports the research project entitled "Improved Accuracy and Robustness for Numerical Partial Differential Equations and Non-Linear Optimization," under the mentorship of a sponsoring scientist. The host institution for the fellowship is Vanderbilt University, and the sponsoring scientist is Dr. David Hyde. This project aims to advance the accuracy and robustness of techniques based on the material point method to model systems of partial differential equations, with applications ranging from weather balloons used in climate research to engineering challenges such as particle-laden flow and avalanches. Furthermore, data-driven formulations are intended to achieve breakthrough results in convergence and accuracy for coupled level set methods in the context of multiphase flow problems such as polycrystalline grain boundary evolution, with applications, for example, to the design of efficient materials for photovoltaic cells. Additionally, the PI and the sponsoring scientist will develop strategies for leveraging novel approaches to obtain sparser and more semantically interpretable solutions for inverse, control, and neural network training problems. The PI will engage in multiple programs for outreach to and recruitment from groups that are under-represented in mathematical and physical sciences. These include advertising projects through websites and programs focused on increasing success and participation of underrepresented populations, working with existing programs at Vanderbilt, and mentoring students from underrepresented groups to access resources available through the Association for Women in Mathematics, as well as technical tracks of the Grace Hopper and Tapia conferences. A quantitative and qualitative evaluation will be conducted to assess the impact of these efforts.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.

该奖项是根据2021年《美国救援计划法》（公法117-2）全部或部分资助的。 Pi Alan Marquez被授予国家科学基金会的数学和物理科学，上升博士后研究奖学金（NSF MPS-ASCEND），以开展与STEM中代表性不足的团体扩大参与的研究和活动计划。在赞助科学家的指导下，与Marquez博士的这一奖学金支持了该研究项目，标题为“提高了数值部分微分方程和非线性优化的准确性和鲁棒性”。奖学金的主办机构是范德比尔特大学，赞助科学家是戴维·海德（David Hyde）博士。该项目旨在根据材料点方法提高技术的准确性和鲁棒性，再到模拟部分微分方程的系统，其应用程序从气候研究中使用的天气气球到工程挑战，例如弹性流量和雪崩等挑战。此外，数据驱动的制剂旨在实现突破性的结果，从而在多相流问题（例如多晶晶元边界演化）的背景下，耦合水平设置方法的融合和准确性，例如，应用于光伏细胞的有效材料的设计。此外，PI和赞助科学家将制定策略，以利用新颖的方法来获得更稀疏，更可解释的解决方案，以解决逆，控制和神经网络培训问题。 PI将从数学和物理科学领域不足的群体中参与多个计划，以进行宣传和招募。其中包括通过网站和计划的广告项目，专注于增加代表性不足的人群的成功和参与，与范德比尔特的现有计划合作，并指导来自代表性不足的小组的学生，以访问数学女性协会的可用资源，以及Grace Hopper和Tapia Charences的技术轨道。将进行定量和定性评估以评估这些努力的影响。该奖项反映了NSF的法定任务，并被认为是使用基金会的知识分子优点和更广泛的影响评估标准的评估值得支持的。