AEM8453: Model Reduction and Approximation of Dynamical Systems

In this course, we will study analytical and data-driven methods for model reduction and approximation of dynamical systems. The focus will be on learning the relevant mathematics and tools for obtaining “lean” low-dimensional representations of dynamical systems, which can be used to facilitate analysis and design. Roughly half of the course will be devoted to the problem of model reduction: i.e., given a mathematical description of a system, reduce the number of degrees of freedom required to faithfully represent that system. The other half of the course will be devoted to data-driven approximation of dynamical systems: i.e., given empirical data generated by a dynamical system, determine a mathematical representation for the underlying system dynamics. Although these two general problems are distinct, they are closely related and will be studied in parallel throughout the term.

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