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ECEN 689 Scientific Machine Learning (Spring 2024)

Instructor: Ulisses Braga-Neto

Course Description: This graduate course provides an introduction to the algorithmic and computational foundations of Scientific Machine Learning (SciML). The course starts with an introduction to scientific machine learning, followed by a brief review of traditional machine learning. The course covers the basics of scientific computation, including ODE and PDE discretization methods, and the basic SciML algorithms: automatic differentiation, physics-informed neural networks, and physics-informed Gaussian processes. Applications to forward prediction, inverse modeling, and uncertainty quantification are presented. Additional material will be discussed through student presentations of selected publications in the area. The course is integrated with, and benefits from, the educational activities of the TAMIDS SciML Lab.

Acknowledgment: The development of this course has been supported by TAMIDS through its Data Science Course Development Program.

Class Contents: (under construction)

Lecture 1: Introduction to Scientific Machine Learning

Lecture 2: Review of Machine Learning

Lecture 3: Introduction to ODE and PDE Discretization Methods

Lecture 4: Automatic Differentiation

Lecture 5: PDE-Constrained Neural Networks

Lecture 6: PDE-Constrained Gaussian Process and Kernel Methods

Lecture 7: Inverse Problems

Lecture 8: Uncertainty Quantification