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| language: |
| - en |
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| 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: |
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| 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: |
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| [ x_{n+1} = r \cdot x_n \cdot (1 - x_n) ] |
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| Where: |
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| x₀ ∈ (0.1, 0.9) is the initial condition |
| r ∈ [2.5, 4.0] controls behavior |
| Label assignment: |
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| 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: |
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| Conv1D → BatchNorm → ReLU × 2 |
| GlobalAvgPool1D |
| Linear → Softmax (via CrossEntropyLoss) |
| Advantages of 1D CNN: |
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| Captures local temporal patterns |
| Learns wave shapes and jitters |
| Parameter-efficient vs. MLP |
| Performance |
| Trained on 500 synthetic sequences (length = 100), test accuracy reached: |
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| 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: |
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| predict_regime(3.95, model, scaler, device) |
| # Output: Predicted Regime: Chaotic (Class 2) |
