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)