Steve Brunton Courses

Dynamical Systems

Explore data-driven discovery and control of nonlinear dynamics with SINDy, Koopman operators, HAVOK analysis, and autoencoders.

• YouTube
• 6 hours
• Self-Paced
• Free Video

Data-Driven Dynamical Systems with Machine Learning

Explore data-driven methods for discovering, representing, and controlling nonlinear dynamical systems with SINDy, Koopman analysis, and deep learning.

• YouTube
• 15 hours
• Self-Paced
• Free Video

Reinforcement Learning

A high-level overview of reinforcement learning methods at the intersection of machine learning and control theory, from dynamic programming and Q-learning to deep RL.

• YouTube
• 3 hours 30 minutes
• Self-Paced
• Free Video

Sparsity and Compression

Explore how sparsity enables compression, compressed sensing, robust regression, sparse classification, and reconstruction of high-dimensional data.

• YouTube
• 4 hours 30 minutes
• Self-Paced
• Free Video

Intro to Data Science

An introductory lecture series linking data science and machine learning to SVD, Fourier analysis, compressed sensing, and data visualization.

• YouTube
• 22 hours
• Self-Paced
• Free Video

Solving the Wave Equation with Separation of Variables and Guitar String Physics

Solve the wave equation by separation of variables, connecting boundary conditions, traveling waves, and guitar-string vibrations and pitch.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Deriving the Wave Equation

Derive the wave equation from Newton’s second law and connect string tension and linear density to a guitar string’s pitch.

• YouTube
• 36 minutes
• Self-Paced
• Free Video

PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation

Solve 2D Laplace’s equation for steady-state heat on a rectangular plate using separation of variables and Fourier coefficients.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

The Curl of a Vector Field - Measuring Rotation

Understand how curl measures local rotation in vector fields, from fluid flow and solid-body rotation to identities involving gradient and divergence.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Sparse Nonlinear Models for Fluid Dynamics with Machine Learning and Optimization

Sparse nonlinear modeling turns complex fluid flows into interpretable, low-dimensional dynamical systems from data.

• YouTube
• 38 minutes
• Self-Paced
• Free Video

Lagrangian Coherent Structures in Unsteady Fluids with Finite Time Lyapunov Exponents

Explore Lagrangian coherent structures in unsteady fluid flows and compute them using finite-time Lyapunov exponent fields.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Sparse Nonlinear Dynamics Models with SINDy - The Library of Candidate Nonlinearities

Learn to design SINDy libraries that encode control, rational dynamics, dimensionality limits, and physical symmetries for sparse model discovery.

• YouTube
• 27 minutes
• Self-Paced
• Free Video

Reinforcement Learning - Machine Learning Meets Control Theory

A high-level introduction to reinforcement learning as a framework for learning control strategies through experience, rewards, Markov decision processes, Q-learning, and hindsight replay.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Complex Analysis - Overview & Motivation, Complex Arithmetic, Euler's Formula & Polar Coordinates

Introduces complex numbers through Euler’s formula, basic arithmetic, and polar coordinates, motivated by oscillatory solutions of differential equations.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Topics in Dynamical Systems - Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos

A high-level tour of how fixed points, linearization, invariant manifolds, bifurcations, and chaos reveal nonlinear dynamical behavior.

• YouTube
• 32 minutes
• Self-Paced
• Free Video