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

该奖项全部或部分根据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上升博士后研究奖学金（NSF MPS-Ascend），以开展与扩大STEM代表性不足的群体参与相关的研究和活动计划。Marquez博士的奖学金支持题为“提高数值偏微分方程和非线性优化的准确性和鲁棒性”的研究项目，该项目由赞助科学家指导。该研究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方法的技术的准确性和鲁棒性，以模拟偏微分方程系统，其应用范围从气候研究中使用的气象气球到充满颗粒的流动和雪崩等工程挑战。此外，数据驱动的配方是为了实现突破性的结果，在多相流问题，如多晶晶界演化的背景下，耦合水平集方法的收敛性和准确性，与应用程序，例如，设计的高效材料的光伏电池。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稀疏和更语义可解释的解决方案。PI将参与多个项目，以推广和招募那些在数学和物理科学方面代表性不足的群体。其中包括通过网站和方案的广告项目，重点是提高成功和参与不足的人口，在范德比尔特现有的方案，并指导学生从代表性不足的群体，以获得通过协会的妇女在数学可用的资源，以及格雷斯霍珀和塔皮亚会议的技术轨道。该奖项反映了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。

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.