Machine Learning and Computational Mathematics
The heart of machine learning is the approximation of functions using finite pieces of data. This is one of the main pillars of computational mathematics. Thus it is not surprising that the success of machine learning in dealing with functions in very high dimensions has opened up some brand new territories in computational mathematics, with potentially unprecedented impact for years to come. In the first part of this talk, I will review some of the most exciting advances of using machine learning to address problems in scientific computing and computational science. In the second part of this talk, I will discuss how machine learning can be formulated as a problem in computational mathematics and how ideas from numerical analysis can be used to understand machine learning as well as construct new machine learning models and algorithms.