Deep Learning to Discover Coordinates for Dynamics: Autoencoders & Physics Informed Machine Learning

Joint work with Nathan Kutz: https://www.youtube.com/channel/UCoUOaSVYkTV6W4uLvxvgiFA

Discovering physical laws and governing dynamical systems is often enabled by first learning a new coordinate system where the dynamics become simple. This is true for the heliocentric Copernican system, which enabled Kepler's laws and Newton's F=ma, for the Fourier transform, which diagonalizes the heat equation, and many others. In this video, we discuss how deep learning is being used to discover effective coordinate systems where simple dynamical systems models may be discovered.

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Some useful papers:
https://www.pnas.org/content/116/45/22445 [SINDy + Autoencoders]
https://www.nature.com/articles/s41467-018-07210-0 [Koopman + Autoencoders]
https://arxiv.org/abs/2102.12086 [Koopman Review Paper]

LearningDiscoverCoordinates