Dynamical Systems

Explore the fascinating world of dynamical systems through a comprehensive series of lectures covering advanced topics such as Sparse Identification of Nonlinear Dynamics (SINDy), Koopman operator theory, compressed sensing, and deep learning applications in dynamics. Delve into practical implementations using MATLAB, analyze chaotic systems like the Lorenz system and logistic map, and discover innovative approaches for modeling complex nonlinear dynamics. Learn about cutting-edge techniques including HAVOK analysis, SINDy autoencoders, and deep delay autoencoders for uncovering latent variables in dynamical systems. Gain insights into energy-optimal trajectories in unsteady flows and robust algorithms for parallel implicit sparse identification of nonlinear dynamics.

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!.