Koopman Operator
A linear operator-theoretic framework for analyzing nonlinear dynamical systems. By mapping nonlinear systems into an infinite-dimensional linear space, it transforms nonlinear problems into linear ones, serving as a core tool for data-driven modeling.
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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.
Koopman operator theory provides a linear analysis framework for nonlinear dynamical systems and has become a core tool for data-driven modeling.
When computing finite-dimensional Koopman approximations using methods such as EDMD, the dictionary must be specified in advance, which is a long-standing difficult problem for researchers.
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Koopman operator theory provides a linear analysis framework for nonlinear dynamical systems and has become a core tool for data-driven modeling.
50%UnverifiedWhen computing finite-dimensional Koopman approximations using methods such as EDMD, the dictionary must be specified in advance, which is a long-standing difficult problem for researchers.
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.
50%