Learning the Brain's Dynamics as a Port-Hamiltonian System
2026-07-11 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors created a mathematical model of brain activity during a wrist movement task, treating the motor cortex like a system that stores and uses energy in a special way. They used brainwave data to train the model, which was able to accurately capture important patterns seen in real brain signals, such as specific power-law behaviors and long-range correlations. Their model can also generate signals that help restore synchrony in brain activity when it gets disturbed, which might help improve brain-computer interfaces by preserving the natural structure of neural signals.
motor cortexbrain-computer interface (BCI)port-Hamiltonian systemphasorspower-law decaygraph neural network (GNN)criticality1/f noisedetrended fluctuation analysis (DFA)phase-locking
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 ($σ\approx1$), $1/f$ 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.