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

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。PI Alan Marquez被授予美国国家科学基金会数学和物理科学提升博士后研究奖学金（NSF MPS-Ascend），以开展与扩大STEM中代表性不足的群体参与相关的研究和活动项目。Marquez博士的研究项目名为“提高数值偏微分方程和非线性优化的准确性和稳健性”，由一位赞助科学家指导。该奖学金的主办机构是范德比尔特大学，赞助科学家是大卫·海德博士。该项目旨在提高基于物质点法的偏微分方程系统建模技术的准确性和鲁棒性，应用范围从气候研究中使用的气象气球到工程挑战，如颗粒流和雪崩。此外，数据驱动的公式旨在在多相流问题（如多晶晶界演化）背景下，在耦合水平集方法的收敛性和准确性方面取得突破性成果，例如应用于光伏电池高效材料的设计。此外，PI和赞助科学家将开发利用新方法的策略，以获得逆、控制和神经网络训练问题的更稀疏和更语义可解释的解决方案。PI将参与多个项目，向数学和物理科学领域代表性不足的群体进行拓展和招募。其中包括通过网站和项目宣传项目，重点是提高未被充分代表的人群的成功和参与，与范德比尔特大学现有的项目合作，指导来自未被充分代表群体的学生通过数学女性协会获得可用的资源，以及Grace Hopper和Tapia会议的技术跟踪。将进行数量和质量评价，以评估这些努力的影响。该奖项反映了美国国家科学基金会的法定使命，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。

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.