Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders
The paper proposes EDMD-kDL, a kernel-based way to learn Koopman embeddings from data without fixing the dictionary in advance.
It combines collocation methods with bilevel optimization to learn both the kernel dictionary and the Koopman approximation. The authors position it against neural-network autoencoder approaches, arguing that kernel methods can be more interpretable and easier to analyze. In numerical tests, including sea-surface-temperature forecasting and video data, EDMD-kDL performs comparably to or better than ANN-based baselines. Its scalability claim rests on kernel matrices tied to collocation points rather than the full training set. ArXiv · AI/CL/LG's note
It combines collocation methods with bilevel optimization to learn both the kernel dictionary and the Koopman approximation. The authors position it against neural-network autoencoder approaches, arguing that kernel methods can be more interpretable and easier to analyze. In numerical tests, including sea-surface-temperature forecasting and video data, EDMD-kDL performs comparably to or better than ANN-based baselines. Its scalability claim rests on kernel matrices tied to collocation points rather than the full training set. ArXiv · AI/CL/LG's note
score 3