GenAIDevTOProd/ChaosMapApproximator

Logistic Map Approximator (Neural Network)

This model approximates the logistic map equation:

xₙ₊₁ = r × xₙ × (1 − xₙ)

It is trained using a simple feedforward neural network to learn chaotic dynamics across different values of r ∈ [2.5, 4.0].

Model Details

• 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

Performance

The model closely approximates x_next for a wide range of r values, including the chaotic regime.

Files

• 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

Applications

• Chaos theory visualizations
• Educational tools on non-linear dynamics
• Function approximation benchmarking

License

MIT License