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

Marquez, Alan, Chula Vista CA

Investigators

Abstract

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.