EDMD-kDL
A data-driven Koopman embedding learning method that combines kernel methods with bi-level optimization. It learns finite-dimensional Koopman embeddings directly from data through a collocation point and bi-level optimization framework, avoiding reliance on neural network autoencoder architectures.
Timeline (last 90 days)
EDMD-kDL (Extended Dynamic Mode Decomposition with Kernel-based Dictionary Learning) is a method proposed in a new paper that, for the first time, systematically combines kernel methods with bilevel optimization to learn a finite-dimensional Koopman embedding directly from data.
In EDMD-kDL, the outer optimization learns the parameters of the kernel dictionary, and the inner optimization solves for a finite-dimensional approximation of the Koopman operator under that dictionary, with the two iterating alternately.
The size of the kernel matrix required by EDMD-kDL depends on the number of configuration points rather than the scale of the training dataset, and therefore it has the scalability for large-scale datasets.
In all tested settings, including global sea surface temperature prediction and learning directly from video data, the performance of EDMD-kDL is either on par with or better than ANN-based methods.
Kernel methods have long received little attention in the Koopman embedding learning setting, and EDMD-kDL reopens the space of possibilities for this direction.
All Facts (5)
In EDMD-kDL, the outer optimization learns the parameters of the kernel dictionary, and the inner optimization solves for a finite-dimensional approximation of the Koopman operator under that dictionary, with the two iterating alternately.
50%UnverifiedThe size of the kernel matrix required by EDMD-kDL depends on the number of configuration points rather than the scale of the training dataset, and therefore it has the scalability for large-scale datasets.
50%UnverifiedIn all tested settings, including global sea surface temperature prediction and learning directly from video data, the performance of EDMD-kDL is either on par with or better than ANN-based methods.
50%UnverifiedKernel methods have long received little attention in the Koopman embedding learning setting, and EDMD-kDL reopens the space of possibilities for this direction.
50%UnverifiedEDMD-kDL (Extended Dynamic Mode Decomposition with Kernel-based Dictionary Learning) is a method proposed in a new paper that, for the first time, systematically combines kernel methods with bilevel optimization to learn a finite-dimensional Koopman embedding directly from data.
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