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MEAM Seminar: “Neural Operator for Scientific Computing”
February 25 at 10:15 AM - 11:15 AM
Accurate simulations of physical phenomena governed by partial differential equations (PDEs) are foundational to scientific computing. While traditional numerical methods have proven effective, they remain computationally intensive, particularly for complex, large-scale systems. This talk introduces the neural operator, a machine learning framework that approximates solution operators in infinite-dimensional spaces, enabling efficient and scalable PDE simulations across varying resolutions and scales. Beginning with the Fourier Neural Operator (FNO) architecture, we explore recent advances in self-supervised learning using scale-consistent learning techniques and modeling complex geometries using adaptive mesh methods. We demonstrate the framework’s practical impact through real-world applications in weather prediction, carbon capture, and plasma dynamics. The talk concludes by examining how foundational tools in computational mathematics can advance efficient architecture design, highlighting the expanding intersection between machine learning, computational science, and engineering.

Zongyi Li
Ph.D. Candidate, Department of Computing and Mathematical Science, California Institute of Technology
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 did 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.