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Reconstructing attractors with autoencoders.

F Fainstein1,2, G B Mindlin1,2, P Groisman3

  • 1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

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This summary is machine-generated.

This study introduces an autoencoder method to reconstruct dynamic system attractors from video, preserving phase space topology. Tested on Lorenz and Rössler systems, it accurately captures complex dynamics.

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Area of Science:

  • Dynamical Systems
  • Machine Learning
  • Computational Physics

Background:

  • Reconstructing dynamic system attractors is crucial for understanding complex phenomena.
  • Existing methods may struggle with preserving topological features from observational data.

Purpose of the Study:

  • To develop and validate a novel autoencoder-based method for attractor reconstruction from recorded footage.
  • To ensure the topological integrity of the phase space is maintained during reconstruction.

Main Methods:

  • Utilized autoencoders for dimensionality reduction and feature extraction from time-series data.
  • Applied the method to video data of the Lorenz atmospheric convection model.
  • Tested on time-series data generated from the Rössler equations.

Main Results:

  • Successfully reconstructed attractors from footage, preserving essential topological characteristics.
  • Demonstrated the method's efficacy on both a geophysical fluid dynamics model (Lorenz) and a chaotic system (Rössler).

Conclusions:

  • The proposed autoencoder method offers a robust approach for attractor reconstruction from observational data.
  • This technique preserves the phase space topology, providing reliable insights into underlying dynamical systems.