Feedback approaches for set-point stabilization of interacting particle systems

What the math gives to ML

The paper contributes a transferable control-theoretic template: treat interacting state variables as a port-Hamiltonian system and synthesize feedback through an instantaneous rolling-horizon energy decrease rather than manually solving a matching equation. Its useful asset for neural networks is the explicit energy-balance viewpoint, which separates conservative motion induced by a potential from damping and a controllable input channel. A practical transfer is a second-order optimizer whose parameter and momentum states follow the paper's position-velocity dynamics, while a short-horizon quadratic control step injects adaptive damping only in selected parameter directions.