Overview

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Explore a comprehensive 15-hour lecture series on data-driven dynamical systems and machine learning. Delve into modern methods for modeling complex systems from data, with a focus on data-driven control. Cover topics such as Dynamic Mode Decomposition, Sparse Identification of Nonlinear Dynamics (SINDy), Koopman Spectral Analysis, and Reinforcement Learning. Learn to simulate systems like the Lorenz System and Logistic Map in MATLAB, and discover how to apply machine learning techniques to fluid mechanics and aeroelastic models. Gain insights into deep learning applications for physics discovery and reduced-order modeling. Understand the integration of optimization algorithms, autoencoders, and physics-informed machine learning in building robust dynamical systems models. Ideal for those interested in the intersection of data science, engineering, and machine learning applied to complex dynamical systems.

Syllabus

Data-Driven Dynamical Systems Overview.
The Anatomy of a Dynamical System.
Simulating the Lorenz System in Matlab.
Discrete-Time Dynamical Systems.
Simulating the Logistic Map in Matlab.
Dynamic Mode Decomposition (Overview).
Dynamic Mode Decomposition (Examples).
Dynamic Mode Decomposition (Code).
Compressed Sensing and Dynamic Mode Decomposition.
Sparse Identification of Nonlinear Dynamics (SINDy).
Sparse Identification of Nonlinear Dynamics (SINDy): Sparse Machine Learning Models 5 Years Later!.
Sparse Nonlinear Dynamics Models with SINDy, Part 2: Training Data & Disambiguating Models.
Sparse Nonlinear Dynamics Models with SINDy, Part 3: Effective Coordinates for Parsimonious Models.
Sparse Nonlinear Dynamics Models with SINDy, Part 4: The Library of Candidate Nonlinearities.
Sparse Nonlinear Dynamics Models with SINDy, Part 5: The Optimization Algorithms.
PySINDy: A Python Library for Model Discovery.
PDE FIND.
Koopman Spectral Analysis (Overview).
Koopman Spectral Analysis (Representations).
Koopman Spectral Analysis (Control).
Koopman Spectral Analysis (Continuous Spectrum).
Koopman Spectral Analysis (Multiscale systems).
Koopman Observable Subspaces & Finite Linear Representations of Nonlinear Dynamics for Control.
Hankel Alternative View of Koopman (HAVOK) Analysis [FULL].
Deep Learning of Dynamics and Coordinates with SINDy Autoencoders.
Data-driven Modeling of Traveling Waves.
Machine Learning for Fluid Mechanics.
Data-Driven Resolvent Analysis.
Data-driven nonlinear aeroelastic models of morphing wings for control.
Deep Learning of Hierarchical Multiscale Differential Equation Time Steppers.
Interpretable Deep Learning for New Physics Discovery.
Kernel Learning for Robust Dynamic Mode Decomposition.
A high level view of reduced order modeling for plasmas.
Promoting global stability in data-driven models of quadratic nonlinear dynamics - Trapping SINDy.
Deep Learning to Discover Coordinates for Dynamics: Autoencoders & Physics Informed Machine Learning.
Sparse Nonlinear Models for Fluid Dynamics with Machine Learning and Optimization.
SINDy-PI: A robust algorithm for parallel implicit sparse identification of nonlinear dynamics.
Reinforcement Learning Series: Overview of Methods.
Model Based Reinforcement Learning: Policy Iteration, Value Iteration, and Dynamic Programming.
Q-Learning: Model Free Reinforcement Learning and Temporal Difference Learning.
Overview of Deep Reinforcement Learning Methods.
Nonlinear Control: Hamilton Jacobi Bellman (HJB) and Dynamic Programming.
Deep Delay Autoencoders Discover Dynamical Systems w Latent Variables: Deep Learning meets Dynamics!.