A two-way street between physics and machine learning

BY SARAH C.P. WILLIAMS

To model systems that change over time and space— in fields from physics and chemistry to economics and computer science— researchers use partial differential equations (PDE). These equations are powerful tools for predicting dynamic changes but are also notoriously complex and difficult to solve.

Aditi Krishnapriyan, who joined the faculty as an assistant professor in Chemical and Biomolecular Engineering in January, is developing methods at both the continuum and atomistic scale. She calls this connection between machine learning and science “a two-way street” where she is utilizing physics knowledge to develop machine learning methods, and machine learning programs, to tackle challenges in physics and chemistry.

“It’s a super exciting area because there’s so much to be done,” says Krishnapriyan. “Historically, researchers in physical and natural science fields have collaborated with theoreticians to model research questions. I’m building a group who will have additional expertise able to work with both areas simultaneously allowing for more nuanced iterative progress to be made more quickly.”

Before joining the College, Krishnapriyan was an Alvarez Fellow in Lawrence Berkeley National Laboratory’s Computational Research Division.

Modeling Materials

She grew up in Iowa, where she was fascinated by how math could describe phenomena in the physical world. At UC Santa Barbara, she started her undergraduate education planning to focus on chemistry. But two years in, she added a second major: physics.

“With physics, I had some great teachers who didn’t just hand us equations and tell us to use them, but actually showed us how to derive results so I understood where the equations came from in the first place,” she recalls.

While some of her classmates enjoyed the experimental aspects of physics and chemistry, Krishnapriyan was drawn to the theoretical side. She joined a research lab studying condensed matter and solid-state physics and began the work of using fundamental physics equations to model the properties of the materials.

“I enjoyed doing the theory work where I would start out thinking through my ideas mathematically with pencil and paper, and then verify the results with computer simulations,” she says.

Integrating Machine Learning

While in graduate school at Stanford, in the lab of Evan Reed, Krishnapriyan continued along the same line of research— computationally modeling solid materials. She became especially interested in how emerging machine learning methods could improve these models. The methods she encountered, however, fell short for the sort of problems she wanted to solve.

“The machine learning methods at the time were mostly developed for areas like computer vision, reinforcement learning, and natural language processing, and didn’t necessarily transfer well to scientific problems” she explains. “I wanted to take ideas from physics and integrate them directly into machine learning so they could be more directly tailored to scientific questions.”

For her Ph.D. in physics, she developed machine learning models that better integrated the rules of geometry and symmetry that physical molecules and materials follow. By adding these new structural parameters, she learned that the models became better at solving partial differential equations.

Her dissertation presented new computational methods for predicting the kinetics of 2D materials— sheets of molecules only a few atoms thick, with properties that differ from thicker, 3D materials.

During and after graduate school, Krishnapriyan thought about working in industry, using her physics-inspired machine learning models to tackle broad scientific problems. She worked first at Google, and then at the Toyota Research Institute. At the time, she enjoyed the experiences in industry and says they helped strengthen her coding skills— and underscored the importance of scientists knowing how to code themselves.

Then, she was awarded the prestigious Luis W. Alvarez Fellowship in Computing Sciences to work as a postdoctoral fellow at Lawrence Berkeley National Laboratory. The opportunity pulled her back to academia.

An Interdisciplinary Lab

Krishnapriyan was attracted to Berkeley, she says, by the plethora of interdisciplin- ary research, and the chance to have a joint appointment in the department of Chemical and Biomolecular Engineering and the department of Electrical Engineering and Computer Sciences. Being among a diverse collection of researchers helps to provide her with fodder for both improving her machine learning models, and ways to apply them to new types of scientific problems.

“Currently I’m teaching a fluid mechanics class. Just in the process of teaching it, I’ve been inspired about new ways we can use machine learning to solve complex partial differential equations.”

Her lab will focus on incorporating physical insights and constraints about a system into machine learning algorithms in a more accurate way than previously possible. She thinks by integrating more physics into algorithms, machine learning can bridge the gap between models and the real world. In the end, she hopes her models help scientists use machine learning in a more useful and accurate way.

“The challenge with machine learning today is that many scientists think the code is sophisticated enough to get a useful model, but the models come up short. Also, researchers don’t always think through what their model can and can’t do,” muses Krishnapriyan. “I am hoping the new methods developed in my lab will make it easier for scientists to take these new algorithms and get more suitable answers.”

ROBERT SAXTON