A Koopman-based framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings

2019/08/30 by Mohammad Amin Khodkar, Khodkar, Mohammad Amin, Pedram Hassanzadeh +4
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #physics.comp-ph #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.1909.00076

arxiv created 2019/08/30 · openalex publication_date 2019/08/30 · arxiv updated 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Spectral Properties of Dynamical Systems, Model Reduction and Decompositions
• Deterministic Nonperiodic Flow
• Determining Lyapunov exponents from a time series
• Spectral analysis of nonlinear flows
• Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
• Clustering of Series via Dynamic Mode Decomposition and the Matrix Pencil Method
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Compressed Convolutional LSTM: An Efficient Deep Learning framework to Model High Fidelity 3D Turbulence

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