Explore deep learning techniques for discovering effective coordinate systems in dynamical systems modeling through this 27-minute video lecture. Delve into the use of autoencoders and physics-informed machine learning to uncover simplified dynamics, drawing parallels to historical scientific breakthroughs like the heliocentric Copernican system. Examine case studies including solar system dynamics, nonlinear oscillators, and partial differential equations. Gain insights into the integration of Sparse Identification of Nonlinear Dynamics (SINDy) with autoencoders, and the application of Koopman theory in machine learning contexts. Access additional resources, including related research papers and the speaker's social media, to further expand your understanding of this cutting-edge approach to physical law discovery and dynamical systems analysis.
Deep Learning to Discover Coordinates for Dynamics - Autoencoders & Physics Informed Machine Learning
Steve Brunton via YouTube
Overview
Syllabus
Intro
Autoencoders
Motivation
General Challenges
Nonlinearity
Fluids
SVD
Auto Encoder Network
Solar System Example
Coordinate Systems
Constrictive Autoencoders
Koopman Review
Nonlinear Oscillators
Partial Differential Equations
Conclusion
Taught by
Steve Brunton
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