Mikaela Mitz, photographed at Lawrence Berkeley National Laboratory (Berkeley Lab), Berkeley, California, 08/03/2022.

Using mathematical techniques to address real-world problems is what drew Mikaela Meitz to applied math as an undergrad. And her passion for the field continues today as she works toward completing her master’s degree in this same discipline.

It also led her to spend the summer with the Data Science Engagement group at the National Energy Research Scientific Computing Center (NERSC) at Lawrence Berkeley National Laboratory, where she focused on applying machine learning methods to address long-standing challenges in the design and evolution of particle accelerators.

“I really enjoy the application of math in the real world, and specifically machine learning,” Meitz said. “Everyone is looking for ways to have computers help us automate and predict things.”

A first-year graduate student at California State University, Long Beach, Meitz worked side by side this summer with Lipi Gupta, a NERSC post-doctoral researcher, to develop a new way of approaching an old problem in particle accelerator design: stability. They believe that machine learning could provide a shortcut to stability prediction.

“This proof-of-principle project is closely related to designing particle accelerators that recirculate particles, and they can have stability issues unless corrected,” Gupta said. “Every time there is a chance for upgrades or a new design of these machines, the process of re-evaluating stability issues begins again, and this becomes very computationally expensive.”

The key to addressing stability issues in accelerator design is particle tracking, Gupta emphasized. “We call the accelerator a lattice. If you make any changes to that lattice, you essentially need to run the entire tracking process over again, and this is what takes the most time.”

So Gupta and Meitz tried a new approach: using physics-embedded Hamiltonian neural networks (HNN) and particle tracking that initially employed simple data based on a “toy problem” – a toy accelerator lattice with just a few elements. They utilized Hamiltonian mechanics so that the neural network can learn conservation laws from the data, which Meitz highlighted in her summer student poster presentation on August 2 at the Lab.

“Particle tracking is an important step in designing particle accelerators,” Meitz said. “What we want to know is, can we use an HNN to train on limited data and track electron particles to advance the design of particle accelerators?”

This is a novel approach that hasn’t been tried before, Gupta noted. “HNNs are one of the best models in terms of performance, and it is pretty exciting because it is so new in this field,” she said.
“We need to do more research and dive a little deeper into this,” Meitz said.

While this initial phase of the project didn’t produce the results they expected, Meitz and Gupta are optimistic about their next steps. “The main thing we found out was that these models we thought were going to perform well surprisingly didn’t, even on very simple data,” Gupta said. “But negative results are still results, and we need to get to the bottom of this.” Following their current diagnostic stage to determine what worked and what didn’t, the next step is to apply their methods to real accelerator data.

The good news is they will continue to collaborate on this research going forward, with Meitz working remotely from Southern California over the next year while she moves into the second year of her master’s degree. In addition, she and Gupta are drafting a paper based on their research findings to date, and Meitz is considering turning this project into her master’s thesis.

Working with Berkeley Lab this summer has been an inspiration, Meitz said. “I mostly worked remotely, but the people in the Data Science Engagement group are very welcoming,” she said. “A lot of the people I worked with this summer have their Ph.Ds., and there is a camaraderie of helping each other learn and grow. Research is a great area to work in, and the people here have helped me gain more confidence. I really appreciate that. I realized this summer that it’s ok if you think you don’t know something.”