【HIMIS Colloquium 学术报告会】
Speaker:
Lingfeng Li
Time:
April 8th, 10:30-11:30am
Location:
HIMIS 7A1
Title:
Neural netwoks methods in scientific computing
Abstract:
I will gives a brief overview of recent neural networks methods for scientific computing, with a focus on solving partial differential equations and learning solution operators. We first compare several neural-network-based PDE solvers, including the Deep Ritz method, physics-informed neural networks, and mixed residual methods. We then discuss the error estimates for different methods and how the optimization methods can affect the accuracy. In the second part, we introduce neural operators for learning mappings between function spaces, and highlight how they can be combined with classical numerical algorithms to achieve high accuracy for general linear problems.