Shyam Sankaran Defends Dissertation on Neural Operators for Modeling Physical Systems

Shyam Sankaran has successfully defended his doctoral dissertation, “Neural Operator Design From a Test-Time Learning Perspective,” under the supervision of Paris Perdikaris, Associate Professor in Mechanical Engineering and Applied Mechanics (MEAM). Sankaran’s research develops more efficient neural operators for modeling physical systems, advancing computational tools that can serve as fast, scalable digital twins.

From Physics-Informed Models to Neural Operators

Sankaran began his Ph.D. in Mechanical Engineering and Applied Mechanics (MEAM) at Penn in January 2021, during the height of the COVID-19 pandemic. Moving to a new country in the middle of winter while classes, research and social interactions remained largely virtual made for an unusual introduction to graduate school.

“Moving to a new country in the dead of winter, confined to an apartment, and doing everything over Zoom during the peak of the pandemic was tough,” Sankaran says. “As things opened back up and campus came alive, Philly warmed up, both literally and socially.”

As he found his footing at Penn, Sankaran began developing methods for digital twins, virtual representations of physical systems that can be used to model and predict their behavior. His early research focused on physics-informed neural networks (PINNs), which incorporate physical laws into the training of neural networks. While powerful, these models can become computationally expensive when applied repeatedly to different versions of a problem.

That challenge led Sankaran to neural operators, which can learn how to solve entire families of problems rather than requiring a new solution process for each individual instance.

“That bottleneck naturally pushed my focus toward neural operators, which learn function mappings directly so that once trained, a new problem instance can be solved almost instantly,” he says.

Sankaran focused particularly on architectures that leverage transformers, the same underlying architecture used in many modern large language models. The rapid development of transformer-based artificial intelligence provided ideas he could adapt and scale for scientific computing. At the same time, access to increasingly powerful computing resources allowed him to test those ideas at a scale he could hardly have imagined when he began his Ph.D.

Research Beyond Penn

Some of his most memorable experiences came from sharing that research beyond Penn. Conferences gave Sankaran an opportunity to meet researchers across the field, exchange ideas and step outside the daily rhythm of graduate research. A 2023 conference trip to Amsterdam with his lab mates stands out in particular.

“Exploring a new city, grabbing food after a long day of talks, and just hanging out made those trips some of the most fun and memorable parts of the entire degree,” he says.

His doctoral research also took him to Argonne National Laboratory, where he had opportunities to run experiments using more than 500 graphics processing units (GPUs). He later returned to Argonne for an internship, giving him another opportunity to apply large-scale computing to scientific problems.

Finding the Right Environment to Explore

For students considering a Ph.D. in MEAM, Sankaran recommends looking beyond a specific research topic when choosing where to study. Because research directions can change considerably over several years, he believes finding the right advisor and lab environment can be just as important.

“Focus on finding an advisor and a lab culture that genuinely fits how you like to work,” he says. “Research directions shift all the time, so having the freedom to explore, test risky ideas, and make mistakes matters so much more than the exact project you start with.”

He also encourages students to embrace MEAM’s interdisciplinary nature and look beyond traditional boundaries between fields.

“Some of the most exciting work happens when you borrow tools from computer science or applied math and bring them into mechanics,” he says. “A Ph.D. is a marathon, and having a supportive lab environment with people you actually enjoy being around makes all the difference.”

Looking Ahead

After graduation, Sankaran will join a startup where he plans to apply ideas developed during his dissertation to real-world problems.

Sankaran extends his gratitude to Perdikaris for giving him the freedom to pursue ambitious ideas, providing access to large-scale computing resources and helping him identify meaningful research questions. He also thanks his committee members, MEAM staff and his lab mates, as well as the friends who made Philadelphia feel like home.

Finally, he thanks his parents for the sacrifices that allowed him to pursue his education and his sister and brother-in-law for their encouragement throughout the difficult moments of his Ph.D.