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arXiv

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

Predicting complex chaotic behaviors using Radial Basis Function Neural Networks

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

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Predicting complex chaotic behaviors using Radial Basis Function Neural Networks

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