Instructor: Ulisses Braga-Neto
Course Description: This course introduces the foundations of Scientific Machine Learning (SciML), a rapidly developing area that brings together the fields of Machine Learning and Scientific Computation. After an introduction to the field, we review the basics of Machine Learning, including neural network and Gaussian process regression, and classical ODE and PDE discretization methods. Next, we discuss automatic differentiation and introduce the main physics-informed methods in SciML, namely, PDE-constrained neural network regression and PDE-constrained Gaussian Process regression. We then present data-driven SciML methods, including operator learning, foundation models, and data-driven reduced-order models. We include throughout the application of SciML methods in forward prediction, inverse modeling, and uncertainty quantification.
Acknowledgment: The development of this course was supported by TAMIDS through its Data Science Course Development Program.
Class Contents: (under construction)