Schedule

MINDS SEMINAR

MINDS Seminar Series | Seungchan Ko (Inha University) - Numerical approximation of PDEs via deep neural networks: analysis and computation

MINDS SEMINAR
period : 2023-03-21 ~ 2023-03-21
time : 17:00:00 ~ 18:00
개최 장소 : Online streaming (Zoom)
Topic : Numerical approximation of PDEs via deep neural networks: analysis and computation
개요
Date 2023-03-21 ~ 2023-03-21 Time 17:00:00 ~ 18:00
Speaker Seungchan Ko Affiliation Inha University
Place Online streaming (Zoom) Streaming link ID : 688 896 1076 / PW : 54321
Topic Numerical approximation of PDEs via deep neural networks: analysis and computation
Contents In recent years, due to the tremendous success of machine learning in various fields, it has recently begun to gain more attention to solve partial differential equations (PDEs) using a deep learning algorithm. In particular, by utilizing the approximation properties of deep neural networks and statistical learning theory to numerical PDEs, this new approach opened a new area of research which is recently called scientific machine learning. In this talk, I will introduce some well-known algorithms in scientific machine learning, for example, Deep Ritz Method or Physics-Informed Neural Network. And then I will also address the mathematical analysis of these methods in the context of the classical numerical analysis framework. Finally, I will introduce my recent result on the analysis and approximation of unsupervised Legendre–Galerkin neural network (ULGNet), which is based on the techniques both from numerical analysis and machine learning. Unlike existing deep learning-based numerical methods for PDEs, the ULGNet expresses the solution as a spectral expansion with respect to the Legendre basis and predicts the coefficients with deep neural networks by solving a variational residual minimization problem. Numerical evidence will also be provided to support the theoretical result.
MinDS MinDS · 2023-03-06 15:57 · Views 448