Sparse Koopman Autoencoders Identify Local Dynamical Regimes in Multibasin Systems

What the math gives to ML

The paper offers a transferable representation-learning principle for systems whose dynamics are only locally linearizable: make the Koopman latent state sparse, so the active-coordinate support becomes an unsupervised regime variable. The useful asset is not merely an L1 penalty, which is standard, but the coupling of sparse supports with a linear latent transition and reconstruction constraint: different basins can occupy different coordinate subspaces instead of being forced into one globally valid linear model. A practical neural implementation is a sparse Koopman autoencoder trained with one-step and multi-step latent prediction losses, followed by support-conditioned diagnostics or local transition operators. The central falsifiable claim is improved long-horizon forecasting and basin identification over a dense-latent Koopman autoencoder at comparable latent width and compute.