Data-driven Koopman mode approximation: A neural power iteration algorithm

What the math gives to ML

The paper's transferable asset is a data-driven power iteration for extracting dominant Koopman observables without constructing a large lifted operator or relying on a manually designed dictionary. This suggests learning latent coordinates that are dynamically simple by repeatedly fitting a neural observable to its own one-step pushforward, with normalization and deflation enforcing nontrivial, distinct modes. In neural networks, the most promising use is a Koopman-mode latent bottleneck for long-horizon prediction, recurrent state-space models, or world models: the learned latent coordinates should evolve approximately linearly and therefore reduce rollout error and stabilize multi-step training.