Applied Mathematics Ph.D. Student Emma Opper Receives the 2026 National Defense Science and Engineering Graduate Fellowship Award

Applied Mathematics Ph.D. student Emma Opper has been selected to receive the 2026 National Defense Science and Engineering Graduate (NDSEG) Fellowship Award. Sponsored by the Air Force Office of Scientific Research (AFOSR), the Army Research Office (ARO), and the Office of Naval Research (ONR) under the Office of the Under Secretary for Research and Engineering, Emma was selected from an applicant pool of 5615 due to her "outstanding achievements in STEM." This award comes with full tuition and fees support, as well as a professional development and travel budget, for 36 months.Ìý

Upon beginning the fellowship this September, Emma will continue work on her proposed research project "NSF++: A Kinetic-Informed Data-Driven Continuum Model for the Space-Atmosphere Interaction Region" under the guidance of Dr. Tomoko Matsuo and Dr. John Evans. This work focuses on improving how scientists model the upper atmosphere in very low Earth orbit. As commercial and national interest in low-orbit satellite operations continues to grow, accurate modeling of this region has become increasingly important and increasingly difficult. In the upper atmosphere, traditional fluid models break down as gas behavior transitions from a smooth, continuum-like flow to a regime where rarefied particle interactions become important and direct simulations become computationally expensive.

Emma’s work aims to bridge this gap by combining physics-based modeling with machine learning. Her work uses high-fidelity kinetic simulations to improve existing continuum models while maintaining computational efficiency. In broad terms, her research sits at the intersection of atmospheric science, fluid dynamics, applied mathematics, and scientific machine learning.Ìý

"The big question motivating me is: can we improve existing continuum models by incorporating more accurate flow physics at only a fraction of the computational cost?"

The project draws on collaborations across multiple disciplines in APPM, including atmospheric science, rarefied-gas physics, machine learning, and continuum modeling. Emma credits much of her development as a researcher to the mentorship and collaborative environment she found within the department.

"I could not have done this without the support I’ve received from the APPM department," she said. "The willingness of the faculty to mentor students both in and out of the classroom, and the amount of time they dedicate to us, genuinely changed my life."

That emphasis on mentorship has become central to how Emma approaches both research and teaching. After committing to graduate school at CU, Emma’s future advisor, Keith Julien, unexpectedly passed away before she arrived on campus. Though the experience was deeply difficult, she says the encouragement he showed her during recruitment continues to shape her confidence moving forward. She later found guidance under advisor Tomoko Matsuo, whose mentorship strongly influenced Emma’s view of what it means to be a scientist.Ìý

"She’s taught me that being a scientist is about far more than just conducting research," Emma said. "It’s also about learning how to write, present, communicate your ideas clearly, and share your passion with others."

Those values reflect a broader mission that Emma describes as "bridging mathematical rigor with clear applications." Before arriving at ̽»¨ÊÓƵ, her research experiences as an undergraduate at UC Santa Barbara ranged from heliophysics and geomagnetism to volcanology and fluid dynamics, experiences that helped shape both her interdisciplinary interests and her enthusiasm for scientific communication. Alongside her research, she has also served as a teaching assistant, mentor, and Lead TA Fellow within the department.Ìý

Receiving the NDSEG Fellowship, Emma says, felt like validation not only of the project itself, but of the collaborative effort behind it.

"I think the application stood out because of the project’s interdisciplinary nature and the excitement behind it," she said. "We’re bringing together topics and scientists spanning applied mathematics, fluid dynamics, atmospheric science, and machine learning to tackle a problem that has both scientific and practical importance."

Looking ahead, Emma hopes to continue pursuing interdisciplinary research while mentoring future generations of scientists and mathematicians. She ultimately hopes to lead large collaborative efforts that call on researchers across disciplines to solve complex, real-world problems.

"More than anything, I hope I can encourage other students to pursue ambitious goals and show them that persistence and genuine enthusiasm for your work can take you a long way."

The Department congratulates Emma on this momentous achievement, and are excited to see the work she produces as a result of the fellowship award.