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Caden Fischer fell in love with math through a high school physics class. It was there he learned that “math is a subject that can describe the world.” 

Its equations can be used to describe many physical phenomena from aerodynamics to smart phones. The May 2025 graduate in mathematics and computer science called math a language that can be spoken in any culture and applied in any setting. 

Persistence is like that, too, and Fischer proved at a young age he had an ample supply of that. Today, Fischer, of Menno, is in his first year of graduate school, pursuing a master’s degree in mathematics. After his junior year, he participated in Research Experience for Undergraduates at �ձ�av��Ƶ. Fischer also was a Future Innovator of America during his senior year. 

But even before he was a college student, Fischer was persistent. 

“I always enjoyed video games and wondered how they worked. How do you take real-world concepts like gravity and put it into a computer?” With that curiosity, it wasn’t surprising the small-town farm boy decided to major in computer science and math. But Fischer wasn’t content to just go to class and hope to learn the answers. 

In the first week of the fall semester before his freshman year, Fischer emailed math professor Jung-Han Kimn, asking about research opportunities. No response. He tried again and still no response. The third email prompted a response, and Fischer began doing research under Kimn in the fall of his freshman year. 

Named Future Innovator of America 

The relationship and Fischer’s persistence helped him to be selected as a Future Innovator of America for the 2024-25 school year.  

Future Innovators is a noncredit research fellowship created by the Jerome J. Lohr College of Engineering. Students work with a project mentor, who must be a faculty or research staff member, to develop and submit a research plan that entails learning by doing. They devote about 10 hours per week to the project. 

Recipients are awarded $5,000 with $4,500 as a stipend and $500 to cover the cost of lab supplies or travel to disseminate the results of their project.  

Fischer’s project was a machine learning challenge that he started the summer before in his Research Experience for Undergraduates program. Working under former computer science assistant professor Kaiqun Fu, Fischer sought to apply physics-informed neural networks to modeling the behavior of biofilm, such as dental plaque, Fischer explained. 

Putting machine learning to work 

The work involved partial differential equations, “which are notoriously difficult to solve” and involve varying rates of change, Fischer said. 

Machine learning can be used to train a computer to undertake the task using artificial neural networks. Fischer’s code was compared with results from a reference numerical method, the Finite Element Method, applied to the Cahn-Hilliard Equation. 

In addition to working with Fu, Fischer also worked with Kimn and Jeffrey Doom from the mechanical engineering department. Finding an answer to the disparity in error rates when running various equations has been challenging, but Fischer appreciates the different approaches offered by three faculty in three different disciplines. 

He said he will continue the work as he prepares a thesis focus for his master’s degree. 

10 weeks at Los Alamos lab 

The Future Innovator work had Fischer well prepared to apply for a summer internship at Los Alamos National Laboratory in New Mexico. He and fellow Jackrabbit Samara Overvaag were accepted for the prestigious nationwide program. “It was pretty cool to represent �ձ�av��Ƶ on a national level,” Fischer said. 

This was the first year for �ձ�av��Ƶ to have two math students at the lab in the same summer. 

Kimn said, “I am very happy that I had another very successful year to send two of my research undergraduate advisees to be Los Alamos.”  

He added that since 2014, the mathematics and statistics department has sent six �ձ�av��Ƶ undergraduate students to national labs after working in the Research Experience for Undergraduate program the prior summer. That includes four to Los Alamos, one to Argonne National Lab and one to the National Center for Atmospheric Research.  

“Two of them continued to work with the same national laboratories during their MS in �ձ�av��Ƶ under my supervision in two summer graduate programs and two academic year-long education programs. 

“All of my undergraduate research advisees have worked hard to set up great qualification to be eligible for national laboratories’ summer research programs. Helping mathematics and statistics undergraduate students to be national laboratories’ students is part of my undergraduate advising activities,” Kimn added. 

Fischer’s Los Alamos internship was in parallel computing. Overvaag’s was in computational physics, similar enough topics that they attended a lot of the same lectures. However, they worked on separate projects. 

Fischer worked with a Ph.D. candidate from the University of Arizona. They worked on writing machine learning algorithms to predict the potential energy field for a given set of atoms. “My part was a small piece in connecting the machine learning model’s uncertainty quantification to the molecular dynamics simulation. In other words, the art of measuring how uncertain you are of a result,” Fischers said. 

For example, this same parallel computing process can be used with meteorological data to predict a certain percentage chance of rain. 

In Fischer’s case, they wanted to predict the potential energy field for a given set of atoms. He called their work basic science that could be applied in a number of fields. 

Paper selected for aeronautics conference 

Fischer noted that work he began with Fu on biofilms crossed field into aerospace. The code he wrote for biofilm simulation also can be used for simulations in fluid dynamics. He proposed a conference paper to the American Institute of Aeronautics and Astronautics. That was accepted and he will present it at the group’s January conference in Orlando, Florida. 

Fischer said his experience at Los Alamos expanded his technical experience in parallel computing. He went having taken a high-performance computing class and having limited experience on �ձ�av��Ƶ’s Innovator high-performance computing cluster, connecting only a couple computers. His work at Los Alamos involved distributive parallel computing with 48 graphic processing units, the equivalent of 48 computers, Fischer said. 

Summer provided career direction 

In addition to that and learning languages used in parallel computing, Fischer said he also met “a bunch of other students who are enthusiastic about parallel computing. Seeing how many incredibly smart people were working there … was definitely a highlight of my time at Los Alamos.” 

Landing a job at Los Alamos or similar national lab is now on his radar along with becoming a professor of mathematics and computational science. 

His advice to his younger peers who have an interest in research: “Ask around. Professors are typically always interested in having students involved in their projects.” 

And if they don’t get an answer right away, be persistent and keep asking.