A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings
arXiv:1909.00076
Abstract
We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the observables are vector-valued and delay-embedded, and the nonlinearities are treated as external forcings. The predictive capabilities of the method are demonstrated for well-known prototypes of chaos such as the Kuramoto-Sivashinsky equation and Lorenz-96 system, for which the data-driven predictions are accurate for several Lyapunov timescales. Similar performance is seen for two-dimensional lid-driven cavity flows at high Reynolds numbers.
References in corpus (10)
- Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
- Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
- Chaos as an Intermittently Forced Linear System
- On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator
- Study of dynamics in post-transient flows using Koopman mode decomposition
- A variational approach to probing extreme events in turbulent dynamical systems
- Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence
- Data-driven prediction strategies for low-frequency patterns of North Pacific climate variability
- Data-driven reduced modelling of turbulent Rayleigh-Benard convection using DMD-enhanced Fluctuation-Dissipation Theorem
- Clustering of Series via Dynamic Mode Decomposition and the Matrix Pencil Method