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A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
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Neural Networks as Geometric Chaotic Maps.

Ziwei Li, Sai Ravela

    IEEE Transactions on Neural Networks and Learning Systems
    |June 30, 2021
    PubMed
    Summary

    Artificial neural networks (NNs) model chaotic dynamics by developing structural chaos. This geometric understanding explains their efficiency in emulating complex, unpredictable systems.

    Area of Science:

    • Dynamical Systems
    • Machine Learning
    • Computational Neuroscience

    Background:

    • Artificial neural networks (NNs) are increasingly used to model chaotic dynamics.
    • A theoretical gap exists in understanding how NNs learn and represent chaotic systems.

    Purpose of the Study:

    • To provide a theoretical understanding of how artificial neural networks (NNs) model chaotic dynamics.
    • To explain the efficiency of NNs in emulating chaotic systems through a geometric lens.

    Main Methods:

    • Employing a geometric perspective to analyze the internal structure of trained NNs.
    • Investigating the network's map as a sequence of geometric operations (stretching, rotation, compression).

    Main Results:

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  • NNs can efficiently model chaotic dynamics by becoming structurally chaotic.
  • A parsimonious NN can reconstruct strange attractors and extrapolate beyond training data.
  • Trained network maps exhibit geometric operations indicative of topological mixing and chaos.

    • Conclusions:

    • NNs are naturally suited for emulating chaotic dynamics due to their inherent structural chaos.
    • The geometric operations within NNs explain their capacity to model complex, unpredictable systems.
    • This study bridges the gap between NNs and the theoretical understanding of chaos modeling.