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README.md

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