Wei Zhu, assistant professor in the College of Natural Sciences's Department of Mathematics and Statistics, was recently awarded a three-year, $450,000 Young Investigator grant by the Air Force Office of Scientific Research to study how scientific machine learning can be used to model enormously complex physical and engineering systems, such as the unsteady fluid flows that make up turbulence.

Wei Zhu, assistant professor of mathematics and statistics
Wei Zhu, assistant professor of mathematics and statistics

“I think of myself as an applied and computational mathematician,” says Zhu. “I’m interested in machine learning and data science, and the math that underlies both, and especially in how we can build trustworthy models with theoretical guarantees when there’s very little data.”

Machine learning is a branch of AI that focuses on how computers can perform complex tasks without constant human input. Like the AI products that have gained prominent attention, such as ChatGPT, machine learning often depends on truly vast datasets to train its models so that they perform reliably. But what happens when you want to use machine learning for an application for which there is very little data available—say, the way an airplane’s wing responds to the turbulence-causing ripples in the air? 

For problems such as this, researchers turn to what is called scientific machine learning, or AI that incorporates established physical and mathematical laws alongside empirical data sets for its power.

"The rationale,” says Zhu, “is that traditional computational models take ages to simulate the system you’re interested in. Conversely, relying solely on sparse data carries significant risk and is unreliable, particularly for high-stakes scientific applications. What is crucial is a seamless integration of both approaches.”

Over the next three years, Zhu will work to speed up the computation of these physical models while ensuring that the models also remain true to physical and mathematical laws. 

“It’s of utmost importance that we figure out how to theoretically guarantee the performance of these models,” Zhu says.

Article posted in Research for Public