Dynamical Systems

This advanced course examines data-driven methods for identifying, representing, analyzing, and controlling nonlinear dynamical systems. Topics include SINDy, Koopman operators, compressed sensing, dynamic mode decomposition, HAVOK analysis, chaotic Lorenz and logistic systems, and autoencoder-based discovery.

Syllabus

Sparse Identification of Nonlinear Dynamics (SINDy).
Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control.
Koopman Observable Subspaces & Nonlinearization.
Koopman Operator Optimal Control.
Compressed Sensing and Dynamic Mode Decomposition.
Hankel Alternative View of Koopman (HAVOK) Analysis [FULL].
Hankel Alternative View of Koopman (HAVOK) Analysis [SHORT].
Magnetic field reversal and Measles outbreaks: HAVOK models of chaos.
Linear model for chaotic Lorenz system [HAVOK].
Simulating the Lorenz System in Matlab.
Discrete-Time Dynamical Systems.
Simulating the Logistic Map in Matlab.
The Anatomy of a Dynamical System.
Deep Learning of Dynamics and Coordinates with SINDy Autoencoders.
Deep Learning of Dynamics and Coordinates with SINDy Autoencoders.
Deep Learning of Dynamics and Coordinates with SINDy Autoencoders.
Finite-Horizon, Energy-Optimal Trajectories in Unsteady Flows.
SINDy-PI: A robust algorithm for parallel implicit sparse identification of nonlinear dynamics.
Deep Delay Autoencoders Discover Dynamical Systems w Latent Variables: Deep Learning meets Dynamics!.