U.S. Naval Research Laboratory Offers Myriad Career Opportunities for Applied Mathematicians

By Lina Sorg

Founded in 1923, the U.S. Naval Research Laboratory (NRL) is the corporate research lab of the U.S. Navy and U.S. Marine Corps. As such, it conducts science and engineering research to develop state-of-the-art technologies and approaches that meet both immediate and long-term U.S. defense needs. Many of NRL’s divisions employ applied mathematicians and computational scientists who work on a variety of interesting projects, from mapping the sea floor to studying the atmosphere and even outer space.

SIAM News recently chatted with Bruce Danly, Director of Research at NRL, and Tegan Webster, head of the Radar Division’s Distributed Sensing Section. During this joint interview, they addressed NRL’s research objectives and aims within the larger Department of Defense (DoD) portfolio, spoke about their individual career trajectories and experiences, and offered advice to early-career members of the SIAM community who wish to pursue employment at NRL or similar institutions.

Tegan Webster, a mathematician at the U.S. Naval Research Laboratory (NRL) and head of the Radar Division’s Distributed Sensing Section, analyzes the graphical user interface of the Multichannel Active Electronically Scanned Array (MAESA) radar testbed in Washington, D.C. The MAESA system transmits, receives, processes, and visualizes data for research and development in radar technology. U.S. Navy photo courtesy of Sarah Peterson.

Bruce Danly: NRL carries out basic and applied research for the Department of the Navy and, more broadly, the DoD. We also do a little bit of work for non-DoD government customers like the National Oceanic and Atmospheric Administration, Department of Energy, and Department of Homeland Security. Our workforce comes from all of the science, technology, engineering, and mathematics (STEM) disciplines, and our projects focus mainly on the pursuit of innovative ideas that will ultimately benefit the nation by enabling the Navy and Marine Corps with cutting-edge technology. Even so, NRL is largely a civilian organization; only about 100 of our 2,500 employees are active-duty military.

SN: What should SIAM News readers know about applied mathematics research at NRL?

BD: Lots of different divisions use mathematics. According to the statistics, we have 11 mathematicians—including Dr. Webster—in the Radar Division alone. Mathematicians are also employed in information technology, electronic warfare, computational fluid dynamics, acoustics, remote sensing, ocean sciences, marine meteorology, and the space divisions. A lot of NRL’s applied math work pertains to data assimilation, specifically the assimilation of large datasets that pair with complex computer models. Think weather prediction, for example.

Fundamentally, we’re working on most of the disciplines that are buzzing right now in science and engineering. Machine learning, artificial intelligence, quantum sensing, and quantum computing are certainly active areas of research at the lab.

SN: What are some of NRL’s current basic research needs?

BD: Statistics, data assimilation, signal analysis, and computer science are the most essential basic research needs, though the generation of new algorithms for signal processing is also important. We conduct a great deal of advanced data assimilation work in meteorology and oceanography. Accurately forecasting sonar propagation and sonar operations in the ocean—which is a very complex environment—requires strong ocean models through which the acoustic waves can propagate. This is a key part of a number of our divisions. Another major component at NRL is the Geographic Information System group, which does a lot of global referencing and represents physical data on different reference grids that model the Earth.

SN: Tell us about your career trajectories. How did you each end up in your current positions?

Tegan Webster: I earned my undergraduate and master’s degrees in applied mathematics and my Ph.D. in mathematics, all at Rensselaer Polytechnic Institute. While in graduate school, I became a student employee in the Radar Division at NRL; the program that I joined is similar to the current STEM Student Employment Program (SSEP). I had done a few internships and the one at NRL was the most interesting, so I stayed on as a full-time employee when I graduated. I spent several years in the Advanced Signal Processing Section, and now I’m the head of the Distributed Sensing Section. I still do technical work in my current position—I specifically work on developing and demonstrating novel radar technologies and concepts—but I also help bring on new hires and student employees. 

BD: My background is in physics, and I came to NRL in my late 30s. Prior to NRL, I had spent my entire career at Massachusetts Institute of Technology (MIT) — both in graduate school and on the research staff. I was working on nuclear fusion at MIT, but I wanted to do something with a payoff that I would see in my lifetime. I joined NRL in 1995 and remained in the Electronics Science and Technology Division until 2008, when I became head of the Radar Division. I worked on high-powered millimeter wave amplifiers for radar applications in the Electronics Division, and I built a high-power 94-gigahertz radar with the Radar Division. I don’t do research myself anymore, but it’s still fun listening to smart people pitch funding proposals.

SN: What does a typical workday look like for each of you?

BD: My workday is that of any administrator in a large organization, from dealing with personnel policy issues and human resource tasks to competing for funding at the lab level. What I’m doing on a given day depends on the time of year. In the fall, I listen to roughly 150 funding proposals, each of which gets 45 minutes. It takes about three months but it’s one of the most enjoyable parts of the job. In the spring, I meet with congressional staff members, and on occasion congressional representatives themselves, to defend how we’re spending our portion of the Navy’s science and technology budget.

I also make connections between our researchers and folks within the Navy and DoD who could integrate an idea or demonstrated advance into something operational. That’s another fun part — it involves playing matchmaker between researchers and other customers.

TW: There’s a ton of variety and flexibility, so it’s hard to get bored. Some days I’ll be onsite working on code, running a simulation, analyzing data, or conducting field testing with our testbed systems or operational radar systems. The Radar Division specifically does a lot of work with the Tactical Electronic Warfare Division and the Remote Sensing Division. 

Sometimes I create briefs and present them to our sponsors because NRL has to bring in its own funding. We also present many of our projects to our research partners, who are typically other government employees or contractors. I frequently collaborate with a team of about five or six people on multiple undertakings, but there are definitely plenty of independent tasks as well, such as coding or documentation.

SN: What advice would you give to students and early-career researchers who hope to pursue a career with NRL or another government laboratory?

TW: I would suggest trying an internship. When I was an early graduate student, I didn’t really think beyond academia because it seemed like the natural path. But internships really changed my perspective, especially the one at NRL because I enjoyed the variety of the work. Every organization—both within and outside of the government—is different and you really won’t know what kind of work it involves unless you experience it for yourself. And if someone wants to stay technical, they should pay attention to whether the established, full-time employees are still doing technical work. At a place like NRL, you can absolutely stay technical throughout your career. 

U.S. Naval Research Laboratory (NRL) mathematician Tegan Webster (right) and NRL electrical engineer Marc Schneider prepare the Multichannel Active Electronically Scanned Array (MAESA) radar testbed for data collection. MAESA handles and visualizes data for research and development in radar technology. U.S. Navy photo courtesy of Sarah Peterson.

BD: NRL has a number of summer internships and hosts between 100 and 200 students every summer, many of whom return to work for us full time. We offer standard DoD student programs like SSEP, and we even have a Science and Engineering Apprenticeship Program for high school students. We have also begun to hire students from several DoD fellowship programs, such as the Science, Mathematics, and Research for Transformation (SMART) Scholarship-for-Service Program. The National Defense Science and Engineering Graduate Fellowship Program awards fellowships to doctoral students in STEM disciplines, and we try to attract these individuals to NRL.

SN: What can you tell us about the hiring process at NRL?

BD: Like many of the defense service laboratories, NRL has direct hire authority; if we find somebody that we want to hire, we can make them an offer without advertising the position. A lot of our hiring is therefore done by word of mouth between hiring managers and people in research divisions who watch graduate students progress in their academic careers and actively recruit them before graduation. However, we’re also starting to participate in more virtual job fairs as we come out of the COVID-19 pandemic. Many NRL divisions are actively recruiting now.

SN: What types of skillsets or particular experiences does NRL look for in prospective employees?

BD: We mainly look for people with master’s degrees and Ph.D.s. There is a premium on advanced degrees and innovators who can come up with original solutions for unfamiliar problems. I don’t do any of the hiring myself, but those who do—section heads like Dr Webster, branch heads, and even division heads—typically want new hires to fill niche roles in their specific sponsored projects. That being said, NRL is not a place with strict swim lanes. People can change divisions or pursue different directions as long as they are able to find funding for their research and it’s germane to something that’s relevant to the sponsor.

TW: Specifically in the Radar Division, it’s good to have a signal processing background. There’s also quite an emphasis on programing, so it really helps to have experience with programming and coding — whether that’s Python, MATLAB, or C++. At a minimum, you’re going to be doing some type of mathematical modeling.

SN: How can SIAM members get involved with NRL collaborations?

BD: A number of our researchers are already involved in SIAM projects, and Steven Rodriguez of NRL’s Material Science Division was selected as a 2023 MGB-SIAM Early Career Fellow earlier this year. Anything that SIAM can do to make the existence of NRL known as a good place for mathematicians to work certainly helps, especially since NRL doesn’t get an appropriated budget to spend on advertising. 

NRL’s Technology Transfer Office can establish educational partnership agreements with universities and industry settings, and we have quite a few cooperative research and development agreements with companies and organizations. We also participate in international collaborations through established project agreements with ally countries like the U.K., Australia, Canada, New Zealand, Germany, and Japan. In addition, I serve as the Navy’s representative on the Science and Technology board for the North Atlantic Treaty Organization (NATO), and NRL frequently collaborates with NATO nations. We’re anything but isolated and we interact with a lot of folks outside of NRL.

SN: What emerging areas of research are a current focus for NRL?

BD: We’re not in the business of building quantum computers—we’re going to let the commercial world do that—but we are making good use of IBM’s existing quantum computers. For the last few years, we’ve had an agreement with the Air Force Research Laboratory (AFRL) for access to IBM’s computers. A previous National Defense Authorization Act and Navy leadership established NRL as the designated quantum center for the Navy, so we recently worked with AFRL, IBM, and the Naval Warfare Centers to come to an agreement that also allows the Naval Warfare Centers to access IBM’s quantum computers. We’re certainly grateful to AFRL because this agreement is going to expand the capacity for quantum computing research. There’s a lot of excitement about quantum computing, which will be very important for certain projects in the future.

SN: Any final thoughts for our readers?

TW: People with a variety of backgrounds can contribute to radar science — you don’t necessarily need to have done graduate research in the field. Many individuals with math backgrounds are well suited to the kind of multidisciplinary work that radar research requires.

BD: NRL is a place where careers take all sorts of unique trajectories through different scientific disciplines because no one area of research is likely to yield the fruits of innovation for a person’s entire career. People will move from one topic to the next, whether they’re physicists or mathematicians or chemists. It’s an exciting place to work, and I have certainly enjoyed working here for 27 years and counting.

Lina Sorg is the managing editor of SIAM News.