NCTS Short Course on Scientific Deep Learning (2023/7/3-8)

This short course discusses various aspects of an important class of scientific machine learning, namely scientific deep learning. To that end, the course will cover the following topics (with certain depths including proofs of relevant theorems):

1) quick review/introduction to optimization and probability,

2) statistical machine learning framework with deep learning,

3) stochastic gradient descents,

4) bias-variance estimation for deep neural network,

5) exploding-vanishing problems in deep learning and methods to overcome these problems. Lecture notes with more in-depth results will be provided.