Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation

The paper models human motor cortex with a port-Hamiltonian and metriplectic formulation. Band-limited neural phasors provide five frequency-resolved sub-energies; phase-locking gates a learned functional connectome, while a GNN surrogate controls state-dependent dissipation. Metabolic input and a fluctuation-dissipation noise channel represent a non-equilibrium steady state. The abstract claims a leakage-free split with three subjects held out from the PhysioNet EEG Motor Movement/Imagery database, reconstruction stability across random seeds, and near-critical avalanche branching with σ≈1. However, the model does not yet reproduce the empirical 1/f spectral slope or long-range temporal correlations. Reported fields “FitTrainN” and “FitTestMSE” remain literal placeholders, limiting quantitative assessment.