# Newest Alvarez Fellow Applies Math, Physics, and Quantum Skills to Renewable Energy

October 30, 2023

By Keri Troutman

Contact: cscomms@lbl.gov

After following a long educational path, Lawrence Berkeley National Laboratory’s (Berkeley Lab’s) newest Alvarez fellow, Erika Ye, is circling back to something she’s been interested in since high school: renewable energy. Informed by an undergraduate degree in electrical engineering, a graduate degree in quantum chemistry, and postdoctoral research at MIT’s Plasma Science and Fusion Center, Ye brings to Berkeley Lab an algorithm she’s developing with the goal of simulating the plasma dynamics key to fusion reactors, promising sources of renewable energy. She is eager to draw on the wealth of mathematics and computing expertise at Berkeley Lab to further her research.

“At MIT I was at a physics lab. It was a great opportunity for getting this project going, but I ended up working by myself a lot,” she said. Through the Alvarez Fellowship, Ye has now joined the Scalable Solvers Group in Berkeley Lab’s Applied Mathematics and Computational Research Division. “It will be great to be at the Lab where there are so many resources and people across scientific and computing fields with whom to collaborate.”

The algorithm that Ye is working on is aimed at solving classical partial differential equations (PDEs) with reduced computational cost. PDEs are used in a wide range of scientific fields to describe all kinds of phenomena. For example, how a fluid flows through a pipe or how extreme weather phenomena occur can be described mathematically using PDEs. The particular PDEs that Ye is interested in—the Vlasov equations—provide a mathematical description of high-temperature plasmas, which are the basis of fusion reactors.

“The sun is a well-known example of a high-temperature plasma,” said Ye. “The operating principle behind fusion reactors, which have become the holy grail for renewable energy, is that you’re containing a miniature sun and harnessing its power.”

That’s a very difficult task of course, and requires a deep understanding of the behaviors of plasmas and how to control and use their magnetic fields. “Understanding plasmas and knowing how to control instabilities are key to figuring out how to confine a plasma,” Ye said. “The computational algorithm that I’m researching has the potential to significantly reduce the computational cost of solving the Vlasov equations, and we have some promising preliminary results on simple test problems that were published last year. Without the algorithm, solving these equations would require a huge amount of supercomputing power.”

"I am excited to have the opportunity to use the supercomputing resources at Berkeley Lab,” Ye said. “Currently, because the algorithm I am developing can solve PDEs with significantly reduced cost, I am able to perform calculations on a single node. However, at some point, I hope to run simulations that are so large that they cannot be solved using standard methods. So having access to the lab's resources and expertise in high performance computing will be very helpful."

## Quantum-inspired Methods

One way of solving PDEs is to determine their value at all points in space—the cost of solving PDEs generally scales with the total number of points. In some cases, the solution to the PDE is very smooth (or even constant), so one does not need many points to describe it. However, the Vlasov equations often require high resolution, so solving them can be prohibitively expensive. The algorithm Ye works with uses quantum-inspired methods to reduce the computational cost of solving Vlasov equations. It was in a quantum chemistry group in graduate school at Caltech where Ye first learned about quantized tensor networks, a computational tool used mainly in quantum chemistry and quantum condensed matter. Ye was motivated to extend these algorithms to a different application, and see if she could use the tensor networks as a quantum-inspired algorithm for simulating plasma dynamics.

“These methods are widely used in quantum simulation but are still very much in their infancy in the context of solving classical PDEs—they seem to work well so far, but we don’t have a lot of explanation about why that is or to what extent they will continue to work,” she said. “Exploring this and being able to implement these ideas and put them into practice in a larger context is something I’m looking forward to working on at the Lab.”

## Finding a Balance

Coming back to the Bay Area was a bit of a homecoming for Ye—she grew up in the South Bay, so is enjoying being close to home again after many years on the East Coast. “My family was always very supportive of me going into science and math,” Ye said. “Both my parents are engineers, so I think that shaped how I think and fostered my general interest in science.” When she’s not immersed in quantum plasma dynamics algorithms, Ye enjoys indoor rock climbing and cooking.

“With this research, I’ve found a good balance of something that’s very motivating in terms of its potential and tangible impact, but also reasonably technical so that I’m continuing to learn new things.” Ye said. “The challenge is that it is a relatively new field, developed separately in quantum chemistry and applied math communities, so there is disjointed work that we would like to unify to ensure that we are working off the best of both.”

“We also don’t yet fully know the boundaries of when the algorithm will perform well, so continuing to investigate it in the context of different PDEs is always useful,” she added. “This is where being at Berkeley Lab with so many different types of scientists will be really helpful.”

Berkeley Lab’s Luis W. Alvarez Fellowship in Computing Sciences offers recent Ph.D.s the opportunity to work on some of the most important research challenges in computing sciences with access to advanced computing tools and expertise at a national Lab. Since its founding in 2002, and in partnership with the DOE Office of Advanced Scientific Computing Research applied mathematics program, the Alvarez Fellowship has cultivated exceptional young scientists who have made outstanding contributions to computational and computing sciences.

**About Berkeley Lab**

Founded in 1931 on the belief that the biggest scientific challenges are best addressed by teams, Lawrence Berkeley National Laboratory and its scientists have been recognized with 16 Nobel Prizes. Today, Berkeley Lab researchers develop sustainable energy and environmental solutions, create useful new materials, advance the frontiers of computing, and probe the mysteries of life, matter, and the universe. Scientists from around the world rely on the Lab’s facilities for their own discovery science. Berkeley Lab is a multiprogram national laboratory, managed by the University of California for the U.S. Department of Energy’s Office of Science.

DOE’s Office of Science is the single largest supporter of basic research in the physical sciences in the United States, and is working to address some of the most pressing challenges of our time. For more information, please visit energy.gov/science.