In 2014, the National Science Foundation launched a new program within the Division of Mathematical Sciences entitled the Enriched Doctoral Training Program (EDT). In this article we highlight recent awards for EDT. All of these projects share the fundamental goal of broadening career options for Ph.D. graduates in the mathematical sciences. However, they differ in the ways in which they propose to achieve this goal and are thus intended to serve as experimental pilot projects, which other institutions may wish to emulate. As the EDT Program Solicitation explains, “Although traditional doctoral training in mathematics has been aimed at an academic career path, recent American Mathematical Society survey data demonstrate that a substantial portion of doctoral recipients are taking positions outside of academia.” The EDT program aims to enhance graduate research experiences for doctoral students, thus preparing them for a variety of academic and non-academic career paths. It supports efforts to engage doctoral students in research activities potentially supplementary to their dissertation research, which would help train them for a broader range of careers and inspire problem-solving in other disciplines through mathematics.
The program encourages collaborations between academic mathematical sciences departments and entities in the business, industry, government, or non-profit realms. Two projects (at the University of Texas at Dallas (UTD) and Princeton University) were funded in the first round of proposals reviewed in 2015, and three more projects (involving the State University of New York at Buffalo, the University of Minnesota, and a collaboration between the University of Wyoming and Colorado School of Mines) were awarded in 2016. In what follows we highlight the main emphasis of each of the 2015 projects; we will detail the 2016 projects in part two of this article, to appear in the December 2016 issue of SIAM News.
The University of Texas at Dallas. Principal Investigator: Sue Minkoff. Co-Principal Investigators: Yan Cao, Yulia Gel, Felipe Pereira, and John Zweck.
The goal of this project is to transform the training of mathematical sciences doctoral students at UTD so that they gain marketable skills and experience developing mathematics and statistics to improve understanding of problems in science and engineering prior to the start of formal thesis research. The 16 doctoral students supported by the project spend two semesters of their second year working on an interdisciplinary research problem posed by one of our external partners from industry, a government lab, or a research institution. Students work in teams of two, along with one mathematics and one statistics faculty mentor at UTD and one external partner. These research projects replace the students’ normal teaching assistant duties in their second year and provide exposure to the entire research cycle. In the summer, after this year-long research endeavor, the students are well positioned to continue work at the external partners’ organizations as interns, thereby gaining experience that could ultimately lead to employment opportunities after graduation.
Students from the 2015-2016 and 2016-2017 EDT projects at the University of Texas at Dallas. From left to right: Conner Davis, Weihua Yang, Daniel Uribe, Samiha Rouf, John Langford, Azar Ghahari, Georgia Stuart, Jonathan Popa, and Cesar Contreras. Not pictured: Kusha Nezafati. Photo credit: Larry Ammann.
Last year, two mathematics students and two statistics students participated in the two EDT projects at UTD, one of which was about uncertainty quantification for seismic inversion. The students began by researching the background for both velocity and microseismic event estimation. In October, we held our first in-person partner meeting with the industry participant (Pioneer Natural Resources), during which both students and faculty gave formal presentations on goals and ideas for tackling the project. These presentations led to a discussion of those aspects of the problem that are most interesting to industry. Subsequent follow-up phone calls and in-person meetings occurred every month or two throughout the year at both Pioneer and UTD, during which students gave status updates, obtained input on direction, and posed questions to the application experts.
All throughout the year, the statistics student learned about previously-unfamiliar topics, including numerical partial differential equations, inverse problems, geophysics, and high performance computing. The mathematics student was exposed to various statistical ideas, including multilevel Bayesian inverse theory and the geophysics application. Our local team at UTD met weekly, and by the end of the year we had simulation software to (1) solve the stochastic velocity estimation problem using a multilevel approximation to the wave equation and (2) apply this theory to real well log data from Pioneer. The students presented their work this summer at the 2016 SIAM Annual Meeting, and their refereed conference paper was accepted for the Society of Exploration Geophysicists’ Annual Meeting, held in October 2016.
Last year’s second EDT project focused on using social media data for infectious disease forecasting, and was in collaboration with RTI International. This project followed a similar timeline: students also gave several talks at meetings, and a refereed conference paper was accepted for the 2016 IEEE BigData Congress. The statistics student on this project ended the year with an internship at MIT’s Lincoln Laboratories.
The projects for the 2016-2017 year involve six students (three mathematics students and three statistics students) and focus on (1) cone beam computerized tomography to acquire patient anatomy data for cancer radiotherapy treatments (external partner: Department of Radiation Oncology, Division of Medical Physics and Engineering, University of Texas Southwestern Medical Center); (2) multisensor tracking of multiple moving targets for defense applications (external partner: Johns Hopkins Applied Physics Laboratory Multisensor Integration Group, Air and Missile Defense Sector); and (3) the impact of climate change on insurance risks using modern deep machine learning algorithms (external partners: Kemper Corporation and NatCatRisk).
EDT: Mathematical Methods for Water Problems
Princeton University. Principal Investigator: Peter Constantin. Co-Principal Investigators: Ning Lin, Simon Levin, and Ignacio Rodriguez-Iturbe.
Professor Ning Lin, assistant professor of civil and environmental engineering at Princeton University, gave a talk to EDT participants titled “Analysis and Modeling of Tropical Cyclone (TC) Climatology.” Photo credit: Tina Dwyer.
Students advised by associated faculty in the Program in Applied and Computational Mathematics at Princeton University form a diverse group, enjoying broad and rigorous graduate training. The EDT activity brings together faculty and students interested in environmental issues, and is centered on the theme of water. Specifically, the research projects range across disciplines, from soil moisture dynamics and cyclones to biogeochemistry and the socio-economics of cooperative management schemes for water-related resources.
The EDT project has multiple dimensions, and has involved collaborative activities among all participants, including EDT fellows, their advisors, and other faculty. In addition to the fundamental research at the interface between mathematics, water, and other environmental problems, students and faculty have been enjoying bimonthly lunch seminars, during which they discuss current research projects. These lunch seminars provide students with feedback, but also serve to broaden the perspectives of both students and faculty. A key element of the project involves placing students in internships at relevant international centers; students have participated in six-week internships to work with researchers at the Centre for Ecological and Evolutionary Synthesis in Oslo, the Universita Ca’ Foscari Venezia and Fondazione Eni Enrico Mattei (FEEM) in Venice, and the Stockholm Resilience Centre.
The follow-up article, to appear in the subsequent issue, will describe the three EDT projects that were funded in 2016, as well as a precursor award funded in 2014.