ACM 270-2 Data-driven methods for dynamical systems: theory and applications
Description: From climate variability to molecular motion and ecological interactions, many complex systems can be understood through the lens of dynamical systems. This course explores modern computational tools for model inference, forecasting, and analysis of dynamical data. Students will develop theoretical understanding of these methods and be able to implement these methods in practice. Topics may include, but are not limited to: dynamic mode decomposition, approximation of transfer and Koopman operators, sparse model inference, kernel methods, and autoregressive modeling. In addition to lectures, students will engage in discussions of recent research papers and complete a project applying these techniques to a scientific application of their choosing.
Note: Many of the methods I discuss are used often for problems in atmosphere-ocean science/geophysical fluid dynamics (as well as in other fields). For sample topics, see the lecture notes from the 2022 WHOI GFD lectures: 2022 WHOI GFD lecture notes.