Faculty Spotlight: Feng Bao

Feng Bao is an associate professor in Florida State University’s Department of Mathematics, part of the College of Arts and Sciences. In 2022, Bao became the first FSU math faculty member to receive the National Science Foundation’s Early Career Development Program (CAREER) award, and he recently began collaborative work to explore geothermal energy, carbon sequestration climate solutions as part of the Department of Energy’s Energy Earthshots initiative. His body of work focuses on data analytics and control methods, and his current research investigates generative artificial intelligence (AI) techniques.

Tell us about your background and what brought you to FSU.

I’m originally from Jinan, the capital of Shandong province in China. I graduated with my doctoral degree from Auburn University in 2014, then worked as a postdoctoral scholar at the Oak Ridge National Laboratory until 2016. From 2016 to 2018, I worked as an assistant professor at the University of Tennessee at Chattanooga. I came to FSU in 2018.

FSU has a good reputation for research, especially in applied and computational mathematics — I have enjoyed my time here. I receive a lot of support from the math department and the university.

What inspired you to choose your field of study?

My primary research focus is on applied and computational mathematics, with an emphasis on stochastic computing, data assimilation, optimal control, and machine learning — all of which are intricately connected to the realm of data science. Stochastic computing is a method of mathematical calculation that treats data as probabilities, and data assimilation is a discipline combining mathematical theory with found observations. Optimal control is an extension of the calculus of variations and the optimization method for deriving control policies. Lastly, machine learning refers to the area that utilizes data and various mathematical techniques (e.g., statistics, linear algebra, probability and calculus) to make predictions and decisions.

I view myself as an applied mathematician. Math can be applied to many areas, and my research motivation stems from a desire to apply mathematical knowledge and skills to address real-world challenges. The field of applied and computational mathematics offers a versatile set of tools applicable across various domains. Guided by this research philosophy, I contribute research outcomes not only to traditional applied and computational math areas, but also to diverse applications across disciplines.

Can you break down your area of research for us?

My research has two aspects: data analytics and control. I develop data analytics methods to explore the information contained in data, and I develop optimal control methods to study how to efficiently act based on the information we extract from data.

The topics my work covers range from abstract mathematical theories to applied practical problems. The applied mathematical tools I’ve been working on are data-driven computational methods and optimization methods, including Bayesian inference, a method used to update the probability of a hypothesis as more evidence becomes available. In addition to the previously mentioned methods, there’s also reinforcement learning, a general method to solving reward-based problems through teaching optimal decision-making, and stochastic gradient descent techniques, which are used alongside other machine learning techniques to find an objective function’s maximum and minimum values.

What is something unexpected that you have learned through your research?

While I don’t often encounter specific surprises in my research, my overall research journey can be characterized as unexpected and full of surprises. My research experience has allowed me to explore science and mathematics, seeking out hidden gems. The unpredictability lies in not knowing precisely what we’ll uncover, and the thrill and excitement come from the surprises and discoveries that emerge along the way.

Do you have any exciting upcoming research projects or goals you are working towards?

Right now, my research team is experiencing exciting research outcomes related to data assimilation problems for weather forecasting and hurricane prediction. Currently, we use complex partial differential equations, PDEs, as weather forecast models to predict how weather systems will evolve. However, to get these models started, we need to accurately measure the starting conditions — this is where data assimilation helps. We’re developing new methods based on diffusion models, one of the most important generative AI techniques in my field, to solve high-dimensional and highly nonlinear data assimilation problems. Effective data assimilation not only plays a key role in accurate data analytics for weather phenomena, but it also holds critical significance in enhancing decision-making processes for mathematicians and weather forecasters alike.

Tell us about your NSF CAREER award and your current projects.

The NSF Early Career Development Program supports my exploration of data-driven feedback control, an area that combines data analytics with optimal control actions. Using the mathematical methods developed with NSF support, I can solve many practical problems scientists and engineers are currently interested in.

This project also aligns closely with my collaborations in the DOE Energy Earthshots initiative. Through extensive partnerships with DOE scientists and engineers, I’ve cultivated a research philosophy centered on applying mathematical principles to address real-world challenges. These collaborative efforts have not only influenced the development of my research methods but have also allowed me the freedom to explore innovative ideas across projects.

Concurrently, I remain dedicated to utilizing methodologies I develop using NSF backing to solve practical problems.

Are there any achievements you hope to accomplish during your career?

Since my career goal is to combine data analytics with optimal feedback control, I hope to first develop powerful data analysis tools for stochastic optimization — which allows me to generate and use random variables — and data assimilation. More specifically, I’m currently developing a class of generative AI-enabled data assimilation techniques to solve real-world weather and climate issues, including data problems related to hurricanes. This would benefit the state of Florida greatly.

What has been the highlight of your career so far?

It’s hard to pick one highlight as there are so many things that I’m excited about. I always feel that the most exciting highlight is just ahead, and I’m eager to capture it.

Do you have any advice for aspiring mathematicians?

Although math is challenging, it’s also fun. The most beautiful thing is often waiting for you to find it. Don’t stop thinking!

If your students only learned one thing from you (of course, hopefully, they learn much more), what would you hope it to be?

I hope they will learn to make plans early and be persistent.