{"ID":6536504,"CreatedAt":"2026-07-14T01:21:01.169441415Z","UpdatedAt":"2026-07-14T18:35:22.803179637Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.10439","arxiv_id":"2607.10439","title":"Learning the Brain's Dynamics as a Port-Hamiltonian System","abstract":"We model human motor cortex during a wrist-extension BCI task as a port-Hamiltonian system (pHS): a conservative interconnection (gyroscopic coupling between neural phasors) plus a dissipative port (power-law energy decay driven by a GNN surrogate). A metriplectic integrator evolves the phasor state; a Fluctuation--Dissipation-consistent noise channel produces stochastic trajectories at body temperature. Training on \\FitTrainN\\ real EEG cycles (PhysioNet EEGMMIDB, 3 held-out subjects) reaches a test MSE of \\FitTestMSE\\ and passes three scale-free criticality rungs: near-critical branching ratio ($σ\\approx1$), $1/f$ power-law spectrum, and long-range DFA correlations. The model generates closed-loop neuromodulation signals that restore phase-locking in silico when applied to de-synchronised inputs, suggesting a path toward structure-preserving BCI decoders.","short_abstract":"We model human motor cortex during a wrist-extension BCI task as a port-Hamiltonian system (pHS): a conservative interconnection (gyroscopic coupling between neural phasors) plus a dissipative port (power-law energy decay driven by a GNN surrogate). A metriplectic integrator evolves the phasor state; a Fluctuation--Dis...","url_abs":"https://arxiv.org/abs/2607.10439","url_pdf":"https://arxiv.org/pdf/2607.10439v1","authors":"[\"Dibakar Sigdel\"]","published":"2026-07-11T18:44:54Z","proceeding":"q-bio.NC","tasks":"[\"q-bio.NC\",\"cs.AI\"]","methods":"[\"Graph Neural Network\"]","has_code":false}