arXiv

A Multi-Branched Radial Basis Network Approach to Predicting Complex Chaotic Behaviours

Predicting complex chaotic behaviors using Radial Basis Function Neural Networks

Built on the work of rssalessio

Radial Basis Functions (RBFs) are a class of mathematical functions widely used in various fields, including machine learning and computational mathematics. These functions are defined based on the distance or similarity between a point and a center, often in a multidimensional space.

They are defined as:

  1. Gaussian RBF: φ(r) = exp(-r^2 / (2 * σ^2))

where r is the distance between the input point and the center, and σ is a parameter controlling the width of the Gaussian.

  1. Multiquadric RBF: φ(r) = sqrt(1 + (r / σ)^2)

where r is the distance between the input point and the center, and σ is a parameter controlling the shape of the function.

  1. Inverse Multiquadric RBF: φ(r) = 1 / sqrt(1 + (r / σ)^2)

where r is the distance between the input point and the center, and σ is a parameter controlling the shape of the function.

  1. Thin Plate Spline RBF: φ(r) = r^2 * log(r)

where r is the distance between the input point and the center.

Proposed Model Architecture

rbfmulti

Trained using Inverse Multiquadratic

Training Parameters

  • epochs = 2000
  • batch_size = 512
  • Prediction Steps = 100

Results

GIFs

Consider citing this work if you find it useful

@misc{sinha2024multibranched,
      title={A Multi-Branched Radial Basis Network Approach to Predicting Complex Chaotic Behaviours}, 
      author={Aarush Sinha},
      year={2024},
      eprint={2404.00618},
      archivePrefix={arXiv},
      primaryClass={cs.LG}
}