Presented by:
Jinchao Xu
Date:
Wednesday 30th October 2019 - 14:05 to 15:05
Venue:
INI Seminar Room 2
Event:
Abstract:
In this talk, I will first give an introduction to
several models and algorithms from two different fields: (1) machine learning,
including logistic regression, support vector machine and deep neural networks,
and (2) numerical PDEs, including finite element and multigrid methods. I will then explore mathematical
relationships between these models and algorithms and demonstrate how such
relationships can be used to understand, study and improve the model
structures, mathematical properties and relevant training algorithms for deep
neural networks. In particular, I will demonstrate how a new convolutional
neural network known as MgNet, can be derived by making very minor
modifications of a classic geometric multigrid method for the Poisson equation
and then explore the theoretical and practical potentials of MgNet.
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