Computational mathematicians occupy a unique position at the Lab, fortifying scientific codes with algebraic and numerical methods, algorithms, solvers, and discretizations. The field abounds with opportunities for researchers like Andrew Gillette, who points out, “Math is more than just crunching numbers. Applying math to scientific problems requires thinking about how data structures are related and what’s possible.”

Within the Center for Applied Scientific Computing’s Numerical Analysis & Simulations Group, Andrew has begun investigating machine learning–driven solutions to mathematical questions, and says this novel intersection of disciplines is analogous to the nascent progress in finite element methods of several decades ago. “When finite element methods were new, there were many different approaches and some surprising successes, but also a lot of skepticism. Today, thanks to coordinated efforts by mathematicians, computer scientists, and engineers, you can easily download tools like the MFEM library and quickly carry out numerical simulations with an expected and reliable performance,” Andrew explains. “Machine learning has achieved wins in different areas of applied math, but people aren’t always sure how to use it or when it’s going to work. Fast forward 20 years, and I expect machine learning will be a common tool of computational scientists, with widespread knowledge of how and when to deploy it effectively.”

Andrew’s current projects range from implicit neural representations in 3D visualization to artificial intelligence in space science. Recent research includes co-developing a computational geometry algorithm that identifies feature scales, estimates uncertainty, and assesses sampling density in large scientific datasets (see the paper preprint and GitHub repository).

Andrew traces his interest in math back to middle school, when a teacher demonstrated a simple shortcut for adding numbers. “It was my first experience with what was essentially a mathematical proof, and it stuck in my mind,” he recalls. After completing a bachelor’s degree at Amherst College, he entered a PhD program at the University of Texas at Austin, intending to focus on number theory.

But the allure of applied mathematics was strong. Andrew says, “I started hearing and reading about exciting ways math was being used in science, and how the formalism and rigor can be beneficial when approaching scientific problems. I learned that you can prove a lot of things with math, but even better is finding mathematical tools that help scientists do their jobs more efficiently.”

Andrew went on to postdoctoral work at UC San Diego, then joined the faculty in the University of Arizona’s mathematics department for six years, eventually earning tenure. While his research at the time focused on finite element methods, his teaching responsibilities included introductory statistics, graduate-level analysis, and “everything in between.” Ready for a career shift, Andrew moved to LLNL in 2019.

“Faculty positions often emphasize independent leadership in research, and career advancement comes by carving out your own niche of research problems and leading a group of students to work on them,” he explains. “The Lab has fewer teaching opportunities, but it’s easier to find research problems and collaborate with experts in all sorts of fields. This has allowed me to expand my research role in a major way.” In particular, Andrew has enjoyed having access to the ideas and possibilities that come from working with a large team.

Even without a classroom, Andrew still finds ways to educate the next generation. He mentors student interns in LLNL’s Computing Scholars and Data Science Summer Institute programs. “Mentoring forces you to communicate clearly and sharpen your own understanding. It’s a rewarding experience that makes your own work stronger,” he notes. Andrew also participates in the Department of Energy’s Computational Research Leadership Council seminar series, which shares innovative research with university students and encourages them to apply for internships at national labs.

Andrew continues to draw inspiration from his graduate school advisor, whose work spanned multiple research areas. “Seeing my advisor enthusiastically approach diverse fields like neuroscience, chemistry, and molecular modeling made me think I could do anything if I found it interesting,” he states. “Whether it’s through publications, the code I write, or people I mentor, my work at the Lab will have an impact.”

*—Holly Auten*