File size: 1,156 Bytes
c6cbad9 8961b4a 86d49d8 8961b4a |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 |
---
license: mit
tags:
- pytorch
- neural-network
- chaos-theory
- logistic-map
language:
- en
---
# Logistic Map Approximator (Neural Network)
This model approximates the **logistic map equation**:
> xβββ = r Γ xβ Γ (1 β xβ)
It is trained using a simple feedforward neural network to learn chaotic dynamics across different values of `r` β [2.5, 4.0].
## Model Details
- **Framework:** PyTorch
- **Input:**
- `x` β [0, 1]
- `r` β [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 |