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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!

Description:

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.

Data-Driven Dynamical Systems with Machine Learning

Steve Brunton

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#Computer Science #Machine Learning #Mathematics #Deep Learning #Reinforcement Learning #Science #Physics #Fluid Mechanics