1. Data-Driven Modeling and Forecasting of Chaotic Dynamics on Inertial Manifolds Constructed as Spectral Submanifolds
- Author
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Liu, Aihui, Axås, Joar, and Haller, George
- Subjects
Mathematics - Dynamical Systems ,Nonlinear Sciences - Chaotic Dynamics - Abstract
We present a data-driven and interpretable approach for reducing the dimensionality of chaotic systems using spectral submanifolds (SSMs). Emanating from fixed points or periodic orbits, these SSMs are low-dimensional inertial manifolds containing the chaotic attractor of the underlying high-dimensional system. The reduced dynamics on the SSMs turn out to predict chaotic dynamics accurately over a few Lyapunov times and also reproduce long-term statistical features, such as the largest Lyapunov exponents and probability distributions, of the chaotic attractor. We illustrate this methodology on numerical data sets including a delay-embedded Lorenz attractor, a nine-dimensional Lorenz model, and a Duffing oscillator chain. We also demonstrate the predictive power of our approach by constructing an SSM-reduced model from unforced trajectories of a buckling beam, and then predicting its periodically forced chaotic response without using data from the forced beam., Comment: Submitted to Chaos
- Published
- 2023