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:
- 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.
- 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.
- 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.
- Thin Plate Spline RBF: φ(r) = r^2 * log(r)
where r is the distance between the input point and the center.
- epochs = 2000
- batch_size = 512
- Prediction Steps = 100
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