# Q&A with AFOSR’s Young Investigator Program Awardee Kaitlyn Muller

Kaitlyn (Voccola) Muller is a research faculty at Colorado State University. In 2014, she was one of the few researchers selected to receive the prestigious AFOSR Young Investigator Program (YIP) award and grant. She recently chatted with her friend, science writer and mathematician Analee Miranda, about what it’s like to collaborate with the Department of Defense (DoD) as a student, post-doctoral researcher, and young investigator.

### What’s your current position?

Research Scientist at Colorado State University.

### What is the focus of your research?

My research focuses on image reconstruction for Synthetic Aperture Radar. I’m interested in developing forward models which incorporate accurate physics while also maintaining a tractable problem that can be inverted. I’m also very interested in modeling scenes of interest by stochastic processes and developing algorithms which utilize statistical methods. Recently, I’ve worked on analyzing how the stochastic nature of the forward model affects the inversion and uncertainty in the results. Finally, I’ve been working on developing an analytic framework to describe the radar inverse problem.

### Why did you apply for the Air Force Office of Scientific Research (AFOSR) Young Investigators Program (YIP)?

I was aware of the Air Force mission very early on in my graduate career. I was introduced to my now program manager, Arje Nachman, while I was still in grad school. I was also an intern at the Air Force Research Lab during summer breaks, so I learned about the YIP before earning my Ph.D. After receiving my Ph.D., I realized it was a good source of funding for my work so I decided I might as well go for it.

### Does your research directly fit with the Air Force mission or did you tailor it specifically for the proposal?

Since I already had experience working with the Air Force and my Ph.D. thesis was related to problems that the Air Force was interested in, I didn’t have to go out of my way to tailor my proposal. My work was already focusing on problems that directly addressed the Air Force mission; they mainly focused on surveillance, remote sensing applications, and detection of object of interest. That’s why it was relatively easy to sell my research as part of the mission, as I was familiar with it.

I find that a lot of math researchers in academia, from more traditional math programs, focus on developing general mathematical theories first, and find applications to their theories later. Your work, as you’ve described it, started with the application first. Do you think that there should be more applied mathematicians in academia who work this way: find open problems in industry or the sciences first and develop or expand upon existing mathematical theory with the clear goal of solving a very specific problem?

I see value in both approaches. I’m more used to having an application given to me and then investigating what mathematical techniques will work for that specific problem. That said, I do think there needs to be general research in applied mathematics, without thinking about the problem first. I think that with less restrictions, a researcher gets a broader view of mathematics and can come up with unique ideas in this open atmosphere without being so application focused. Later, someone like me might realize that this math is useful for her very specific application. I think that applied math research from either direction is very useful.

### What kind of value do you think an applied mathematician brings that is vital to the success of basic research for the DOD?

I think most people, when they think about DoD research, think the research is focused on solving a specific problem; that is focuses on needs in the here and now and must be solved in a timely manner. Of course, this is the kind of research that I like to do. I’m very application focused and I enjoy finding or developing math that fits. This kind of applied math research work is valuable for the current issues the DoD is facing. The DoD also needs to think about future issues. I think it’s also important to invest in basic research because we don’t know what kind of math is going to be needed for future problems. Applied mathematicians can do this type of research too in the DoD. We need people working on general math that is less focused on what the Air Force needs now and more on what may be needed in the long term.

### How have the issues with Congress, wanting to decrease basic research funding, affected your decision to apply for funding?

It is disappointing. I think that any decrease in basic research funding hinders the scientific process. Most of the useful techniques that helped me solve current defense application problems came from people doing basic research in the past. Maybe these mathematicians didn’t realize their work was going to be applied to Air Force or radar research, but you need basic research before you can solve an application, most of the time. I think Congress is hindering science and technology advancement by cutting basic research funding, and having a very short-sided view of what’s needed for scientific superiority.

### What does an applied mathematician need to know before submitting a proposal to the AFOSR?

Like I mentioned earlier, I was lucky to know what the Air Force mission was and what they were interested in long before I graduated. I think most applied mathematicians are not aware of Air Force missions, their open problems, and the additional constraints that come with working with a very specific application. You can’t assume everything is a sphere; you can start there but in the end, for it to be truly useful, you should include realistic assumptions. I think learning about the types of problems the Air Force is interested in and acknowledging the constraints that will be put on you to work on real applications is important. Researchers interested in Air Force funding should talk to the scientists and program managers at the Air Force Laboratories, find out what they’re working on and what they’re interested in. They should also try to attend program reviews for different funding agencies in order to figure out what’s currently being done and how their research can uniquely advance the Air Force mission.

### What is expected from a mathematician who receives a YIP award from the AFOSR?

YIP funding is actually pretty general so my goal is just putting out publications and going to conferences. I do like to put a little bit of emphasis on the fact that my work is supported by the Air Force and that there are interesting open mathematical Air Force problems, especially when I’m at a conference. If I’m organizing a session, I like to try to bring together the Air Force community with the applied math community, so they’re talking to each other and realizing that they have similar goals. Trying to bring together the two communities is my own goal, but overall the funding has very basic academic goals: publications and conference attending; I don’t need to deliver any software.

### What do you use your YIP grant on?

I use it for my salary and my travel to conferences. I’ve also funded a visiting researcher to our university for a year to work on problems that fit under my proposal.

### In your opinion, how important are grants and funding for mathematical research?

I don’t think it’s as important as for other fields because most mathematicians don’t necessarily need the specialized equipment that non-mathematical researchers need to advance their work. Funding is obviously nice to have because you’re provided with the ability to travel to other math departments and go to conferences to learn about what other researchers are doing and to share your ideas. That’s just as important as doing your own research - talking to other people. A mathematician can also use the funding to support graduate students and visiting researchers, who can work on your problems so you can do more with them than what you can do on your own.

### What are your plans for future research and do they include continuing to work with the Air Force?

Yes. I like working on radar problems with the Air Force. I’m not ready to abandon that field yet. I feel like there are a lot of interesting open math problems in the Air Force and I personally have future work to consider. I want to improve my stochastic analysis toolbox by adding more uncertainty variables and seeing how each new variable affects the general inversion process and the specific radar inverse problems I’m interested in. For example, I’m interested to see if the inversion technique can handle more complex imaging scenarios and complex media. I’m interested in fully understanding the polarimetric radar modality, which incorporates additional wave polarizations in the forward problem instead of using a standard scalar wave equation approach. Ultimately I’d like to branch out to other imaging modalities and signal processing applications and see how I can improve their usefulness in more complex environments.

### What advice would you give a current applied math graduate student about future research and funding? What about a recent grad or new professor/researcher?

I would say, in terms of funding, try to figure out what funding opportunities are out there that relate to your research interests. I researched funding opportunities and found the National Research Council postdoctoral program and the AFOSR YIP that I’m currently supported on while I was still a graduate student. I knew about them before I was even close to applying to them. This helped me prepare for the application process. I knew that I would have to come up with my own ideas instead of just relying on ideas from my advisor. This forced me to prepare myself to write proposals and applications for these types of grants. What helped me the most to prepare for proposal writing is a piece of advice that someone on my thesis committee gave me: to keep a research journal and write down all my research ideas as they came to me. When I was finally ready to put together a cohesive proposal for projects in my research area, I went through that journal, read all my old ideas and picked out the ones that were most promising. My advice to a young researcher would be to keep coming up with ideas and keep track of them because you may not remember them in the future.

### Do you have any suggestions on how SIAM can improve communications between the DOD and SIAM members?

What I do personally, and what Margaret Cheney, my doctoral advisor, taught me to do, is to always invite DoD people to speak at SIAM conferences so that the mathematicians of SIAM know about the applications that DoD Labs are funding and interested in. This also helps the DoD see cutting edge applied math research that they may need. Personally, I think SIAM could advertise more broadly and try to get in touch with researchers at government labs, bring them to conferences and promote the funding opportunities that are available from the DoD and other agencies. I remember that I found the NRC postdoc opportunity on my own. I think I found the AFOSR YIP on my own as well. I don’t think SIAM makes it very obvious that DoD opportunities are available to young mathematicians. There are also many NRC opportunities to visit labs for mid- and high-level career scientists, during sabbaticals and summer breaks.

You can find out more about The National Academies of Science, Engineering, and Medicine, and in particular, the National Research Council (NRC) fellowships here.

You can find out more about AFOSR’s research opportunities, including the Young Investigator Program here.

Note: The YIP award is not restricted to AFOSR; other government agencies and national laboratories, such as DARPA, the Department of Energy, the Office of Naval Research, and the National Institutes of Health, have similar awards.