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Measure-preserving EDMD: A 4-line structure-preserving & convergent DMD algorithm!
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Research Abstract by Matt Colbrook, Cambridge University
We introduce measure-preserving extended dynamic mode decomposition (mpEDMD), a data-driven algorithm that enforces measure-preserving truncations of Koopman operators using a general dictionary of observables. It is flexible and easy to use with any pre-existing DMD-type method and with different data types. As well as convergence to the spectral properties of the underlying Koopman operator (for general measure-preserving dynamical systems), mpEDMD has improved stability and qualitative behavior of trajectories. For delay embedding, mpEDMD even comes with explicit convergence rates as the size of the dictionary increases. We demonstrate mpEDMD on a range of challenging examples, its increased robustness to noise compared with other DMD-type methods, and its ability to capture the energy conservation and statistics of a turbulent boundary layer flow with Reynolds number greater than 60,000 and state-space dimension greater than 100,000.
We introduce measure-preserving extended dynamic mode decomposition (mpEDMD), a data-driven algorithm that enforces measure-preserving truncations of Koopman operators using a general dictionary of observables. It is flexible and easy to use with any pre-existing DMD-type method and with different data types. As well as convergence to the spectral properties of the underlying Koopman operator (for general measure-preserving dynamical systems), mpEDMD has improved stability and qualitative behavior of trajectories. For delay embedding, mpEDMD even comes with explicit convergence rates as the size of the dictionary increases. We demonstrate mpEDMD on a range of challenging examples, its increased robustness to noise compared with other DMD-type methods, and its ability to capture the energy conservation and statistics of a turbulent boundary layer flow with Reynolds number greater than 60,000 and state-space dimension greater than 100,000.
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Measure-preserving EDMD: A 4-line structure-preserving & convergent DMD algorithm!
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