MPS-Ascend: Structure-Preserving Algorithms and Their Applications in Plasma Physics

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 Allen Alvarez Loya被授予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计划。这项奖学金授予Alvarez Loya博士，以支持题为“MPS-Ascend：结构保存算法及其在等离子体物理学中的应用”的研究项目，该项目由一位赞助科学家指导。该奖学金的主办机构是洛斯阿拉莫斯国家实验室，赞助科学家是唐琪博士。在这个项目中，PI Alvarez Loya将考虑两种方法来开发高效和准确的算法，这些算法可以在数值模拟中保留重要的物理或数学结构。第一种方法是无散度可扩展MHD求解器。第二种方法是基于参数化哈密顿系统的保结构神经网络。所提出的工作的关键部分是一个参数化的辛神经网络，它具有可证明的近似性质，显著地推广了该领域以前的工作。为了扩大MPS领域的参与，PI带来了他自己作为参与项目的学生的经验，如科罗拉多大学的BOLD（通过领导力和多样性拓宽机会）项目和加州州立大学的PUMP（通过指导博士培养本科生），以及在指导代表性不足的少数群体学生方面的大量记录。与赞助科学家唐博士一起，PI将共同指导LANL的本科生和研究生。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 Allen Alvarez Loya 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. Alvarez Loya supports the research project entitled "MPS-Ascend: Structure-preserving algorithms and their applications in plasma physics", under the mentorship of a sponsoring scientist. The host institution for the fellowship is the Los Alamos National Laboratory, and the sponsoring scientist is Dr. Qi Tang.In this project PI Alvarez Loya will consider two approaches to developing highly efficient and accurate algorithms which preserve important physical or mathematical structures in numerical simulations. The first approach is a divergence-free scalable MHD solver. The second approach is based on structure-preserving NNs for parameterized Hamiltonian systems. The critical piece of the proposed work is a parameterized symplectic neural network that has a provable approximation property significantly generalizing previous work in the area. To broaden participation in MPS fields, the PI brings his own experience as a participating student in programs such as University of Colorado's BOLD (Broadening Opportunity through Leadership and Diversity) program and California State University's PUMP (Preparing Undergraduates Through Mentoring towards PhDs) as well as a substantial track record in mentoring students from under-represented minority groups. Along with the sponsoring scientist Dr. Tang, the PI will co-mentor undergraduate and graduate students at LANL.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.