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language: |
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- en |
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Chaos Classifier: Logistic Map Regime Detection via 1D CNN |
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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) |
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1 → Periodic (oscillates between repeating values) |
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2 → Chaotic (irregular, non-repeating behavior) |
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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 |
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Financial systems often exhibit regime shifts: stable growth, cyclical trends, and chaotic crashes. |
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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 |
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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 |
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r ∈ [2.5, 4.0] controls behavior |
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Label assignment: |
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r < 3.0 → Stable (label = 0) |
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3.0 ≤ r < 3.57 → Periodic (label = 1) |
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r ≥ 3.57 → Chaotic (label = 2) |
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Model Architecture |
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A 1D Convolutional Neural Network (CNN) was used: |
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Conv1D → BatchNorm → ReLU × 2 |
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GlobalAvgPool1D |
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Linear → Softmax (via CrossEntropyLoss) |
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Advantages of 1D CNN: |
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Captures local temporal patterns |
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Learns wave shapes and jitters |
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Parameter-efficient vs. MLP |
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Performance |
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Trained on 500 synthetic sequences (length = 100), test accuracy reached: |
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98–99% accuracy |
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Smooth convergence |
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Robust generalization |
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Confusion matrix showed near-perfect stability detection and strong chaos/periodic separation |
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Inference Example |
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You can generate a prediction by passing an r value: |
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predict_regime(3.95, model, scaler, device) |
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# Output: Predicted Regime: Chaotic (Class 2) |
