{
  "id": "2310.06067",
  "version": "v1",
  "published": "2023-10-09T18:19:00.000Z",
  "updated": "2023-10-09T18:19:00.000Z",
  "title": "Data-Driven Modeling and Forecasting of Chaotic Dynamics on Inertial Manifolds Constructed as Spectral Submanifolds",
  "authors": [
    "Aihui Liu",
    "Joar Axås",
    "George Haller"
  ],
  "comment": "Submitted to Chaos",
  "categories": [
    "math.DS",
    "nlin.CD"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-09T18:19:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral submanifolds",
      "data-driven modeling",
      "chaotic attractor",
      "largest lyapunov exponents",
      "nine-dimensional lorenz model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}