# Chaos Classifier: Logistic Map Regime Detection via 1D CNN

This model classifies time series sequences generated by the **logistic map** into one of three dynamical regimes:

- `0` → Stable (converges to a fixed point)
- `1` → Periodic (oscillates between repeating values)
- `2` → Chaotic (irregular, non-repeating behavior)

The goal is to simulate **financial market regimes** using a controlled chaotic system and train a model to learn phase transitions directly from raw sequences.

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## Motivation

Financial systems often exhibit regime shifts: stable growth, cyclical trends, and chaotic crashes.  
This model uses the **logistic map** as a proxy to simulate such transitions and demonstrates how a neural network can classify them.

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## Data Generation

Sequences are generated from the logistic map equation:

\[
x_{n+1} = r \cdot x_n \cdot (1 - x_n)
\]

Where:
- `x₀ ∈ (0.1, 0.9)` is the initial condition
- `r ∈ [2.5, 4.0]` controls behavior

Label assignment:
- `r < 3.0` → Stable (label = 0)
- `3.0 ≤ r < 3.57` → Periodic (label = 1)
- `r ≥ 3.57` → Chaotic (label = 2)

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## Model Architecture

A **1D Convolutional Neural Network (CNN)** was used:

- `Conv1D → BatchNorm → ReLU` × 2
- `GlobalAvgPool1D`
- `Linear → Softmax (via CrossEntropyLoss)`

Advantages of 1D CNN:
- Captures **local temporal patterns**
- Learns **wave shapes and jitters**
- Parameter-efficient vs. MLP

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## Performance

Trained on 500 synthetic sequences (length = 100), test accuracy reached:

- **98–99% accuracy**
- Smooth convergence
- Robust generalization
- Confusion matrix showed near-perfect stability detection and strong chaos/periodic separation

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## Inference Example

You can generate a prediction by passing an `r` value:

```python
predict_regime(3.95, model, scaler, device)
# Output: Predicted Regime: Chaotic (Class 2)