Numerical Twin with Two Dimensional Ornstein--Uhlenbeck Processes of Transient Oscillations in EEG signal

Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity as a two-dimensional Ornstein-Uhlenbeck (OU) process with three interpretable parameters: decay rate, mean frequency, and noise amplitude. We develop two complementary estimation strategies. The first fits the power spectral density, amplitude distribution, and autocorrelation to recover OU-parameters. The second segments burst events and performs a statistical match between empirical spindle statistics (duration, amplitude, inter-event interval) and simulated OU output via grid search, resolving parameter degeneracies by including event counts. We extend the framework to multiple frequency bands and piecewise-stationary dynamics to track slow parameter drifts. Applied to electroencephalography (EEG) recorded during general anesthesia, the method identifies OU models that reproduce alpha-spindle (8-12 Hz) morphology and band-limited spectra with low residual error, enabling real-time tracking of state changes that are not apparent from band power alone. This decomposition yields a sparse, interpretable representation of transient oscillations and provides interpretable metrics for brain monitoring.