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Deep Koopman

Koopman autoencoders: learning coordinates where nonlinear dynamics turn linear

Paper title Deep learning for universal linear embeddings of nonlinear dynamics

Lusch et al. (University of Washington) · Aero & CFD · General PDEs · Public: code

Paper arXiv 1712.09707PDF

An autoencoder whose latent coordinates are trained to evolve linearly: the encoder maps the state to a few coordinates, a matrix advances them one time step, and the decoder maps back. Three losses enforce reconstruction, linear evolution in the latent space and accurate multi-step prediction. For systems whose frequency changes with amplitude, a small auxiliary network supplies the eigenvalues as a function of the latent state.

Published
Nature Communications

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