| --- |
| license: mit |
| tags: |
| - pytorch |
| - neural-network |
| - chaos-theory |
| - logistic-map |
| language: |
| - en |
| --- |
| # Logistic Map Approximator (Neural Network) |
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| This model approximates the **logistic map equation**: |
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| > xₙ₊₁ = r × xₙ × (1 − xₙ) |
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| It is trained using a simple feedforward neural network to learn chaotic dynamics across different values of `r` ∈ [2.5, 4.0]. |
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| ## Model Details |
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| - **Framework:** PyTorch |
| - **Input:** |
| - `x` ∈ [0, 1] |
| - `r` ∈ [2.5, 4.0] |
| - **Output:** `x_next` (approximation of the next value in sequence) |
| - **Loss Function:** Mean Squared Error (MSE) |
| - **Architecture:** 2 hidden layers (ReLU), trained for 100 epochs |
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| ## Performance |
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| The model closely approximates `x_next` for a wide range of `r` values, including the chaotic regime. |
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| ## Files |
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| - `logistic_map_approximator.pth`: Trained PyTorch model weights |
| - `mandelbrot.py`: Full training and evaluation code |
| - `README.md`: You're reading it |
| - `example_plot.png`: Comparison of true vs predicted outputs |
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| ## Applications |
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| - Chaos theory visualizations |
| - Educational tools on non-linear dynamics |
| - Function approximation benchmarking |
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| ## License |
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| MIT License |
