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--- |
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license: mit |
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tags: |
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- pytorch |
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- neural-network |
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- chaos-theory |
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- logistic-map |
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language: |
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- en |
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--- |
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# 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 |
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- **Input:** |
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- `x` ∈ [0, 1] |
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- `r` ∈ [2.5, 4.0] |
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- **Output:** `x_next` (approximation of the next value in sequence) |
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- **Loss Function:** Mean Squared Error (MSE) |
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- **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 |
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- `mandelbrot.py`: Full training and evaluation code |
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- `README.md`: You're reading it |
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- `example_plot.png`: Comparison of true vs predicted outputs |
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## Applications |
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- Chaos theory visualizations |
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- Educational tools on non-linear dynamics |
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- Function approximation benchmarking |
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## License |
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MIT License |
