# Mathematician fellow looks at unexpected behavior in software algorithms

*Meet Anadil Rao*

Science fiction can inspire the imagination, and for Anadil Rao, it was science fiction and documentaries on the Discovery Channel which first captured his curiosity in childhood. So, he took to science, technology, engineering and mathematics (STEM) by going into mathematics.

“I felt a calling to explore the deep structure that lies within simple mathematical facts,” said Rao.

He wanted to explore how a federal laboratory functioned and joined on with the National Science Foundation’s (NSF) Mathematical Sciences Graduate Internship Program (MSGI), through the Oak Ridge Institute for Science and Education (ORISE). He studied under his mentor, Balu Nadiga at Los Alamos National Laboratory (LANL), in the Computational Physics and Methods Division.

The NSF MSGI Program provides research opportunities for mathematical sciences doctoral students, allowing them to participate in internships at national laboratories. NSF MSGI seeks to provide hands-on experience for the use of mathematics in a nonacademic setting.

Rao’s main area of study was the Stein Variational Gradient Descent (SVGD) sampling method. The SVGD is used as an alternative to the Markov Chain Monte Carlo method, which is an algorithm used, in part, for computing probability. Both algorithms are used in software, machine learning and neural networks. However, SVGD is more useful in many scenarios. Rao looked at cases where SVGD did not behave as expected and researched ways to mitigate the issue. The NSF hopes to use SVGD in climate change modeling, so it is necessary that it works as expected.

To accomplish this, Rao used two approaches. In his first approach, he ran a large number of experimental tests which used various parameters to try and isolate the specific issues. In his second approach, he studied the theoretical underpinnings of the SVGD algorithm, looking for ways in which its behavior could become pathological. Both approaches provided insights into the observed pathological behavior of SVGD and allowed him to develop methods to remedy such behavior.

While at LANL, Rao had the benefit of researching in “the fishbowl,” a hall where dozens of other visitors and interns collaborate. He bounced ideas and solutions off his fellow interns, allowing for a plentiful scientific interaction. Additionally, Rao improved his computational and coding skills during the fellowship.

“It opened me to the possibility of using methods of applied mathematics to questions of pure mathematics,” explained Rao. “Thus, it expanded my horizon on the perspectives one can take to address pure mathematical questions.”

Today, Rao is earning his doctoral degree from Northeastern University. He credits NSF MSGI as being the inspiration for two topics he is now studying which relate to string theory. He recommends the program to others STEM students looking to learn the intricacies of federal facilities.

“Aspiring scientists who really want to see fruits of their labor change the world should consider interning at a federal facility. Even more so if one is uncertain and divided between an academic track type job or a career that is on the cutting edge of technology.“

*The NSF MSGI Program is funded by NSF and administered through the U.S. Department of Energy’s (DOE) Oak Ridge Institute for Science and Education (ORISE). ORISE is managed for DOE by ORAU.*