Neural Operator for Scientific Computing

Zoom link for remote attendees

Meeting ID: 999 4631 3276 Passcode: 123123

Abstract:

Scientific computing, which aims to accurately simulate complex physical phenomena, often requires substantial computational resources. By viewing data as continuous functions, we leverage the smoothness structures of function spaces to enable efficient large-scale simulations. We introduce the neural operator, a machine learning framework designed to approximate solution operators in infinite-dimensional spaces, achieving scalable physical simulations across diverse resolutions and geometries. Beginning with the Fourier Neural Operator, we explore recent advancements including scale-consistent learning techniques and adaptive mesh methods.  We demonstrate the real-world impact of our framework through applications in weather prediction, carbon capture, and plasma dynamics, achieving speedups of several orders of magnitude.

Bio: Zongyi Li is a final-year PhD candidate in Computing + Mathematical Sciences at Caltech, working with Prof. Anima Anandkumar and Prof. Andrew Stuart. His research focuses on developing neural operator methods for accelerating scientific simulations. He has completed three summer internships at Nvidia (2022-2024). Zongyi received his undergraduate degrees in Computer Science and Mathematics from Washington University in St. Louis (2015-2019). His research has been supported by the Kortschak Scholarship, PIMCO Fellowship, Amazon AI4Science Fellowship, and Nvidia Fellowship.