A Physics-Inspired Classical Digital Twin of Cortical Dynamics: A Band-Stratified Metriplectic Port-Hamiltonian Neural Network Learned from Brain-Computer-Interface EEG

What the math gives to ML

The paper's transferable asset is an explicit energy-based factorization of a dynamical system: conservative interactions use a skew-symmetric operator, while dissipation uses a positive-semidefinite operator. This creates a recurrent or neural-ODE layer whose passivity and unforced energy decay are structural consequences of its parameterization, rather than properties learned through a fragile penalty. The most direct ML application is a stable latent state-space block for long-horizon forecasting, world models, or closed-loop control.