Joe Kileel Recipient of the 2025 Distinguished Researcher Award

Joe Kileel is the 2025 recipient of the Peter O’Donnell, Jr., Distinguished Research Award, acknowledging Kileel’s “outstanding research records and impressive and sustained contributions to the Oden Institute, and for the distinction his work and reputation brings to the Oden Institute and The University of Texas at Austin.”

An assistant professor of mathematics and Principal Faculty at the Oden Institute for Computational Engineering and Sciences, Kileel’s research focuses on developing computational models that exploit the underlying algebraic and geometric structure of given problems. 

“This award is an indicator that others are finding interest in my research. When I got the email notification, it was not something on my radar. It was a very pleasant surprise,” said Kileel. The award provides $100,000 in funds over a four-year period used at the researcher’s discretion to support research at the Oden Institute. 

Kileel, who is a member of the Center for Scientific Machine Learning at the Oden Institute, said the funds will provide support for his research group’s activities within the applied math and scientific machine learning groups and may be used to fund student travel and/or provide summer support. 

With research projects that have broad applications across scientific imaging, computer vision, machine learning and inverse problems, Kileel’s work leverages algebraic and geometric structure to improve computational methods and to develop mathematical guarantees. The computational methods make complex data processing more efficient and accurate.  

“I try to develop algorithms that exploit algebraic or geometric structure to reduce how much data needs to be stored, or speed up convergence, etc. Scalability in high dimensions may not be possible in general; part of the research is identifying problem classes where it can be achieved. If successful, it translates into less runtime, and possibly being able to do things on desktop computers that would otherwise need clusters of computers (or not be doable).”

A recently-awarded 2025 Sloan Fellowship recipient, Kileel acknowledged it has been a gratifying year. He said for him, part of being a researcher is finding creative ways to explore problems.

Kileel says his approach to computational math is somewhat non-traditional. “My foundations are actually in algebraic and geometric areas of math – tools that are not so often used in applications. I have been able to connect them to applications and algorithms. Lots of things are nonlinear and when using algebraic methods, such as low-rank tensor methods or multivariate polynomial solving methods, we may obtain a better model.”

“Of course, there are others doing related work, but it's not the most traditional part of applied and computational mathematics. I think there's a lot to be gained by bringing richer models and tools to the subject. In some sense, this is also what machine learning is doing.  Neural networks are, in a less understood way, modeling low dimensional, non-linear dependencies and spaces as well,” he added.

Kileel’s work on tensor methods, nonconvex optimization, methods to solve polynomial systems of equations, and manifold learning “enables efficient and accurate data analysis for problems that are not well modeled by purely linear models,” he said. 

His research also has real-life applications. Kileel has contributed to methods in cryo-electron microscopy, which concerns reconstruction of molecules from large data sets of noisy measurements. Other concrete applications of his research include computer vision and robotics, “where one is trying to combine information in 3-D reconstruction pipelines as used in Google Street View or by self-driving cars.”

In addition, Kileel is collaborating on developing digital twins for drug trials. Working with Karen Willcox, Oden Institute Director, and Thomas Yankeelov, lead of the Center for Computational Oncology at the Oden Institute and a professor of biomedical engineering, Kileel’s contribution includes investigating reduced ordering modeling (ROM) based on nonlinear manifolds or algebraic varieties, which may enable more accurate use of the digital twin. “A piece of this project includes seeking ways to increase the safety of drugs for users in drug trials. We are very early in the project, which started in December 2024,” said Kileel.

Selecting good research directions takes “a bit of vision,” Kileel thinks. “There’s a wide space of things we could work on. Choosing  novel directions, things other researchers didn’t emphasize or missed, directions that may be impactful – these choices are significant parts of research.” 

Taking a fresh approach to applied mathematics means forging a path that is sometimes less traveled, and progress isn’t always steady. “At times there can be very quick progress.  Alternatively, research can move in a sideways direction. I like to take on projects where I don't know what the answer will be or how the project will turn out. I kind of enjoy the surprises as they occur.”

Kileel currently mentors five Ph.D. students at UT (three in the Math Department and two in the Oden Institute’s CSEM program). Prior to joining UT as an assistant professor, Kileel completed his postdoctoral training at Princeton University. 

The Peter O’Donnell, Jr., Distinguished Researcher Awards Program was created in 2011.