Omejc, N.; Roman, S.; Todorovski, L.; Dzeroski, S.

Neural population models are widely used to interpret electroencephalography (EEG), yet their relationships remain far less systematically understood than those among single-neuron models. More fundamentally, it remains unclear whether EEG can support a uniquely plausible population-level mechanism, or whether multiple structurally distinct models can explain the data equally well. To address this question, we combine comparative analysis of canonical model families with grammar-based generation of new candidate architectures. We assembled 17 canonical neural mass and phenomenological models and embedded them in a shared structural space. From their common processes, we defined a probabilistic grammar over interpretable dynamical components and developed ENEEGMA (Exploring Neural EEG Model Architectures), a Julia-based framework for grammar-based model generation, simulation, and parameter optimization, to generate additional candidate models. We then assessed both canonical and generated models by fitting them to EEG independent-component spectra from four datasets for each condition: resting state and steady-state visual evoked potentials. Canonical models formed six structural clusters. Across conditions, compact low-dimensional polynomial oscillators performed best overall, with Montbrio-Pazo-Roxin, FitzHugh-Nagumo, and Stuart-Landau models offering the best balance of fit quality, stability, and simplicity. Grammar-based exploration further showed that the space of viable EEG node models extends beyond canonical formulations: even a restricted search over 1,000 generated models produced compact alternatives competitive with nearly all canonical families and achieving the strongest cluster-level SSVEP fits. Together, these findings suggest that EEG spectra constrain plausible neural population mechanisms without uniquely determining them. Beyond this, grammar-based model exploration provides a principled, data-driven framework for EEG-constrained model discovery.