Epilepsy Modeling Based on EEG Data Using Neural Singular ODE Systems

To model highly oscillatory processes (for example, processes determined by the rhythms of electroencephalograms (EEG) measured at certain points in the cerebral cortex), a special system of neural singular ordinary differential equations (NSODE), the trajectories of which exhibit chaotic behavior for certain parameter values, has been designed. Further, a special algorithm for minimizing the loss function was used to adjust the parameters of the NSODE system.The presented algorithm demonstrates an effective approach to the identification of parameters of nonlinear dynamical systems of the NSODE type in the context of EEG modeling. The success of the approach is due to the synergistic combination of numerical optimization methods, including the regularized Gauss-Newton method with SVD decomposition of the corresponding matrices, adaptive tuning of optimisation parameters and complex control of numerical stability. Also important is the multi-level analysis of the quality of the results, which includes both traditional statistical metrics and modern visualization methods. The obtained modeling results were then used to predict epileptic seizures in patients under observation.