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

2026-07-11

AI Summary

This work proposes a structure-preserving modeling approach to characterize the dynamic evolution of motor cortex activity during brain–computer interface tasks. Cortical dynamics underlying wrist extension are formulated as a port-Hamiltonian system, integrating gyroscopic-coupled neural phase oscillators, a graph neural network–driven energy dissipation mechanism, and a noise channel satisfying the fluctuation–dissipation theorem to emulate stochastic neural activity at physiological temperatures. This study presents the first application of the port-Hamiltonian framework to electroencephalographic (EEG) dynamics, employing a metriplectic integrator to enable physics-informed, structure-preserving learning and generate closed-loop control signals capable of restoring phase synchrony. Evaluated on hold-out EEG data from three subjects, the model achieves low FitTestMSE error, successfully passes criticality assessments via branching ratio, 1/f spectral scaling, and detrended fluctuation analysis (DFA), and effectively reconstructs phase locking from desynchronized inputs in silico.

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.

Problem

• port-Hamiltonian system
• motor cortex dynamics
• brain-computer interface
• criticality
• phase-locking

Innovation

• port-Hamiltonian system
• metriplectic integrator
• Fluctuation-Dissipation theorem
• criticality
• neuromodulation