[공모전/홍보] [학과 세미나 개최 안내] Neural Networks for Solving PDEs: A Brief Review and Some Recent Explorations
Speaker: Prof. Xiaotian Gao, Assistant Professor, Zhongguancun Academy
Title: Neural Networks for Solving PDEs: A Brief Review and Some Recent Explorations
Time: June 15, 11:00 AM – 12:00 PM
Place: 36-106A
About the Speaker
Prof. Xiaotian Gao is an Assistant Professor at Zhongguancun Academy. Previously, he was a Senior Researcher at Microsoft Research Asia and a Research Scientist at Intel Labs China. He received his Ph.D. in Electrical Engineering from Harbin Institute of Technology in 2018.
Abstract
Partial differential equations (PDEs) are the language of modeling in science and engineering, yet classical numerical solvers are often computationally expensive and struggle with high dimensionality, multi-scale phenomena, and the need to solve repeatedly under varying conditions. Deep learning has recently emerged as a promising alternative, broadly organized along two complementary directions: approximating the solution of a single PDE instance, as in physics-informed neural networks; and learning solution operators that map between function spaces and generalize across an entire family of PDEs, as in neural operators.
In this talk, I will first give a brief and necessarily selective review of these ideas and their fundamental trade-offs—in particular, the tension among optimization difficulty, reliance on simulated data, and computational cost. I will then share a few of our own explorations along this line, which attempt to make physics-driven neural solvers more efficient to train, less dependent on costly simulation data, and more scalable through decomposition and parallelism. I hope to close with some broader thoughts on physics-driven machine learning, and on how such tools might connect to the PDEs encountered in plasma and fusion research.
