As CSEM Graduate Student Rui Fang approaches the end of her fifth year at the Oden Institute for Computational Engineering and Sciences, her journey through the realm of scientific machine learning reveals a narrative of persistence, discovery, and ambition. Rui, a dedicated Computational Science and Engineering Mathematics (CSEM) graduate student, has been navigating the intricate world of Hamiltonian systems under the mentorship of Richard Tsai, Oden Institute core faculty and mathematics professor.
Rui’s research is rooted in the field of scientific machine learning. Her focus is on optimizing simulations for Hamiltonian systems, a fundamental class of physical systems in classical mechanics. The goal of her work is to tackle the computational inefficiencies that arise in multi-scale simulations, where both time and spatial scales vary significantly.
“Simulating multi-scale problems requires very fine grids, which can be computationally expensive,” Rui explains. “We’re working on improving efficiency through parallelization in time and using machine learning techniques to approximate numerical integrators. It’s a challenging but exciting endeavor.”
Parallelization in time, one of Rui’s main strategies, involves dividing computational tasks into smaller chunks that can be processed simultaneously. This is particularly tricky due to the causal nature of time-based simulations, where each time step depends on the previous one. On the other hand, incorporating machine learning models—especially deep neural networks—into simulations aims to reduce the cost of evaluating complex functions, offering a novel approach to enhancing computational performance.
Beyond her research, Rui has been enjoying some new hobbies.
“I recently learned how to crochet and knit,” said Rui. “ I started crocheting for the first time in 2023 when I finished my thesis proposal, because, you know, it's quite a milestone. I wanted to find something new to fill my time with. I started crocheting some toys, and several months later, I began to learn how to knit and started knitting myself scarves and sweaters. That's very fun.”