@Article{CSIAM-AM-1-4,
author = {Weinan, E and Ma, Chao and Wu, Lei and Wojtowytsch, Stephan},
title = {Towards a Mathematical Understanding of Neural Network-Based Machine Learning: What We Know and What We Don't},
journal = {CSIAM Transactions on Applied Mathematics},
year = {2020},
volume = {1},
number = {4},
pages = {561--615},
abstract = {<p style="text-align: justify;">The purpose of this article is to review the achievements made in the last
few years towards the understanding of the reasons behind the success and subtleties
of neural network-based machine learning. In the tradition of good old applied mathematics, we will not only give attention to rigorous mathematical results, but also pay attention to the
insight we have gained from careful numerical experiments as well as the analysis of
simplified models. Along the way, we also list the open problems which we believe to
be the most important topics for further study. This is not a complete overview over
this quickly moving field, but we hope to provide a perspective which may be helpful
especially to new researchers in the area.</p>},
issn = {2708-0579},
doi = {https://doi.org/10.4208/csiam-am.SO-2020-0002},
url = {https://global-sci.com/article/82388/towards-a-mathematical-understanding-of-neural-network-based-machine-learning-what-we-know-and-what-we-dont}
}