Machine Learning: Mathematical Theory and Scientific Applications
E Weinan · Notices of the American Mathematical Society · 2019
This is essentially the transcript of the Peter Henrici Prize Lecture, given on July 15 at ICIAM 2019 in Valencia.The talk was designed to give a broad overview of• some of the current work on integrating machine learning with scientific modeling (e.g.physicsbased modeling) to address some of the most challenging problems in a variety of disciplines, and • some of the current work on building a mathematical theory of machine learning.There were two basic messages that I wanted to convey.First, in theoretical and computational science and engineering, a fundamental obstacle that we have encountered is our limited ability to deal with problems in high dimension.Machine learning has now provided new tools for