Synthetic Data Generation

The QSynthetic class provides generators for 20+ dynamical regimes.

Basic Usage

import QSignature
syn = QSignature.QSynthetic()

# Exponential decay
t, R = syn.exponential_decay(tau=2.0)

# Underdamped oscillator
t, R = syn.underdamped_oscillator(alpha=0.2, omega_d=6.0)

# Overdamped system
t, R = syn.overdamped_system(tau1=0.5, tau2=3.0)

# Conservative oscillator
t, R = syn.conservative_oscillator(omega0=2*np.pi)

Available Systems

Method	Description
exponential_decay()	First-order exponential relaxation
underdamped_oscillator()	Underdamped harmonic oscillator
overdamped_system()	Overdamped or critically damped system
conservative_oscillator()	Undamped (conservative) oscillations
duffing_oscillator()	Nonlinear Duffing oscillator
powerlaw_decay()	Power-law/heavy-tailed decay
chaotic_system()	Lorenz or Rössler chaotic systems
fractional_order_system()	Fractional order differential equations
chirp_system()	Time-varying frequency (chirp)
multiscale_system()	Multiple interacting temporal scales
intermittent_system()	Bursty/intermittent dynamics

Adding Noise

# Add Gaussian noise during generation
t, R = syn.underdamped_oscillator(alpha=0.2, omega_d=6.0, noise_std=0.05)

# Add noise after generation
R_noisy = syn.add_measurement_noise(R, noise_type='gaussian', std=0.1)

Sampling Irregularities

t_irr, R_irr = syn.add_sampling_irregularities(t, R, missing_prob=0.05)

Batch Dataset Generation

dataset = syn.generate_dataset(n_samples=100, add_noise=True, noise_std=0.05)