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

• URL: http://arxiv.org/abs/2607.10439v2
• Date: Fri, 17 Jul 2026 05:07:27 GMT
• Title: Learning the Brain's Dynamics as a Port-Hamiltonian System: A GNN-Surrogate Metriplectic Twin for Non-Equilibrium Cortical Dynamics and Closed-Loop Neuromodulation
• Abstract summary: We model human motor cortex, recorded during rest and motor-imagery BCI conditions, as a port-Hamiltonian system.<n>A metriplectic formulation places the resting cortex at a non-equilibrium steady state sustained by an explicit metabolic port.<n>We score the free-running model against model-independent dynamical invariants it did not author.
• Score: 0.09229852843814058
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: We model human motor cortex, recorded during rest and motor-imagery BCI conditions, as a port-Hamiltonian system: a conservative interconnection (skew-symmetric coupling between band-limited neural phasors) together with a dissipative port whose state-dependent decay is set by a graph-neural-network surrogate. The Hamiltonian is resolved into five interpretable frequency sub-energies, and a phase-locking prior measured from the recordings gates the learned functional connectome so that coupling is admitted only where phase coherence is present. A metriplectic formulation places the resting cortex at a non-equilibrium steady state sustained by an explicit metabolic port, with a fluctuation-dissipation-consistent noise channel governed by a single arousal temperature. Fitting the model to 'FitTrainN' phasor samples from the PhysioNet EEG Motor Movement/Imagery database, under a leakage-free split with three subjects held out entirely, yields a held-out kinematic reconstruction error of 'FitTestMSE' that is stable across random seeds. We then score the free-running model against model-independent dynamical invariants it did not author: it reproduces near-critical avalanche branching ($σ\approx1$) but not yet the aperiodic $1/f$ spectral slope or the long-range temporal correlations of real cortex a concrete, falsifiable gap that we trace to specific, testable upgrades. The port-Hamiltonian structure supplies neuroanatomically grounded stimulation ports with stability guarantees, positioning the model as a physically principled, structure-preserving substrate for closed-loop neuromodulation.

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