Topics in Applied Mathematics: Machine Learning Methods in Scientific Computing

This course will cover various machine learning methods that are used and developed in the field of scientific computing. The basics of standard scientific computing methods for solving partial differential equations, such as the finite difference method or spectral method will be covered. Machine learning methods including principal component analysis, clustering methods, deep neural networks will be introduced. Reduced and physics-informed models resulting from a combination of these methods will be the focus of this course. Prerequisites: Math 217, Math 309, Math 449, or the permission of the instructor.