| # 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. | |
| --- | |
| ## 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. | |
| --- | |
| ## 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) | |
| --- | |
| ## 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 | |
| --- | |
| ## 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 | |
| --- | |
| ## 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) | |