Neural population models for EEG: From Canonical models to alternative model structures.

Neural population models are widely used to interpret electroencephalography (EEG), yet the relationship between the two remains far less systematically understood as compared with 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 assemble 17 canonical neural mass and phenomenological models and embed them in a shared structural space. From their common processes, we define a probabilistic grammar over interpretable dynamical components and develop ENEEGMA (Exploring Neural EEG Model Architectures), a Julia-based framework for grammar-based model generation, simulation, and parameter optimization. With this grammar, we generate additional candidate models. We then assess both canonical and generated models by fitting them to EEG independent-component spectra from four datasets for two conditions, i.e., resting state and steady-state visual evoked potentials (SSVEP). Canonical models form six structural clusters. Across conditions, compact low-dimensional polynomial oscillators perform best overall, with generalized Montbrió-Pazó-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 produces compact alternatives competitive with nearly all canonical families, with the generated cluster achieving the strongest Bayesian expected rank for SSVEP fits. These findings suggest that EEG spectra constrain classes of plausible population-level dynamical architectures without uniquely determining them and that grammar-based model exploration provides a principled, data-driven framework for EEG-constrained model discovery.