Mathematics doctoral student earns National Science Foundation research fellowship

Jonathan Thompson, PhD student in Mathematics, was recently awarded a prestigious research fellowship from the National Science Foundation (NSF) to pursue studies in predicting flash-flood behaviors.

“We hope to create a new mathematical model which is capable of inferring the physics of fast- and slow-moving flood flows based on real and simulated data,” Thompson explained. “From there, we plan to use current models of slow-moving floods as a validation tool for our model to verify that it agrees with existing models.”

Thompson’s idea for this research came about after he attended a presentation on physics-based neural networks by CU Boulder professor Maziar Raissi in 2021.

“I had just started my graduate program at that point, but I knew from that day on that I wanted to be involved in researching the utility of scientific computing techniques which blend machine learning and physics to solve novel problems,” said Thompson. “My academic background is in math and physics, but my professional background is in software engineering; physics-informed machine learning sits right in the intersection of the subjects I’m most passionate about, so it feels like a perfect match.”

While receiving this fellowship is exciting on its own, it has an extra layer of accomplishment for Thompson as he took a break from education after his undergrad to focus on his athletic career in ice dance, for which he competed in the 2014 U.S. Figure Skating Championships at the Novice level. Thompson knew returning to academia and catching up in his studies posed a challenge, so he tried to keep his expectations tempered and concentrate on doing his best.

“I used to be a pretty competitive person, so letting go of results and focusing on the process was pretty hard for me,” said Thompson. “By the time I applied for this fellowship, I was mainly interested in getting practice and feedback for writing research proposals for the NSF. Since a considerable amount of academic research is funded by the NSF, the Graduate Research Fellowship Program felt like an invaluable opportunity to gain that experience. To actually have been awarded this fellowship is almost like having a dream come true that I had made peace with letting go of, and that is one of the most humbling things I’ve ever experienced.”

Another significance to the fellowship is its personal aspect for Thompson.

“Almost exactly a year ago, I lost my dad very suddenly and unexpectedly,” Thompson shared. “He was an integral part of my most positive experiences with mathematics and the sciences, and we shared a very strong bond over our love for STEM. The arduous process of applying for this fellowship became a way to process through that loss and connect with him by reflecting on those formative experiences and how the people we love continue to impact the world through those they inspire even after they’re gone. Receiving this fellowship feels like I’ve been given an incredible opportunity to honor those experiences with him by carrying that energy into research that I know he’d have loved to hear about.”

Along with Thompson’s NSF and ice dance accomplishments, he was awarded the Outstanding Undergraduate Student Awards for both Applied Mathematics and Physics at 19 in 2013 and the 2022 UCCS Graduate School Research Fellowship, and has been instrumental in helping the math department develop.

“Everyone recognizes Jonathan’s humble personality and collegiality among his peers,” said Radu Cascaval, UCCS Mathematics professor and Thompson’s advisor. “Jonathan already made a huge impact in the department, helping create the UCCS Math Clinic and conducting workshops on machine learning for peer students. His passion for math and science is contagious. The NSF award will help him find the right balance of academic rigor applied to solving real world problems that have a societal impact.”

Though Thompson’s ultimate goal with this research is to better predict fast-moving flood behaviors for improved humanitarian aid and damage control, he’s prepared for the possibility that his research may uncover more questions than answers but is looking forward to learning more and seeing what is unearthed along the way.

“With research, it’s generally the case that the questions that are answered are rarely the ones we go in asking,” Thompson stated. “I think it’s reasonable to think that we might be able to uncover other questions – and maybe answers, if we’re really lucky – about the efficacy of particular machine learning approaches in modeling the behavior of real-world phenomena. Because the real world is so much more complex than controlled lab environments, accurately modeling real-world phenomena has historically been quite difficult – we hope to explore the capabilities and limitations of machine learning in adapting known physical knowledge to the evolution of these complex systems.”

“I’m excited to be wrong, I’m excited to be right, but mostly I’m excited to explore ideas.”

About the UCCS College of Letters, Arts & Sciences

The College of Letters, Arts & Sciences at UCCS is the university’s largest college, enrolling nearly 6,000 students across 21 departments and programs. The college offers 19 majors and 53 minors in the arts, humanities, social sciences and natural sciences. Students can also choose from five accelerated bachelor’s and master’s degrees, nine full master’s degrees and three Ph.D. degrees, as well as pre-medical and pre-law programs. The mission of the college is to position graduates for success in their personal and professional lives, with a focus on thinking, creating and communicating — skills vital to employers and graduate and professional schools. Learn more about the College of Letters, Arts & Sciences at UCCS.