Learning the Brain's Dynamics as a Port-Hamiltonian System

Dibakar Sigdel

Learning the Brain's Dynamics as a Port-Hamiltonian System

Neurons and Cognition 2026-07-11 v1 Artificial Intelligence

Authors: Dibakar Sigdel

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 ( $\sigma\approx1$ ), $1/f$ 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.

Cite

@article{arxiv.2607.10439,
  title  = {Learning the Brain's Dynamics as a Port-Hamiltonian System},
  author = {Dibakar Sigdel},
  journal= {arXiv preprint arXiv:2607.10439},
  year   = {2026}
}