Bilevel optimization for data-driven learning of Koopman embeddings using kernel-based autoencoders
The paper introduces Extended Dynamic Mode Decomposition with Kernel-based Dictionary Learning (EDMD-kDL) to learn finite-dimensional Koopman embeddings directly from data. It combines collocation methods and bilevel optimization to simultaneously learn a kernel dictionary and the Koopman approximation. This method outperforms standard ANN approaches in various nonlinear system modeling tasks.