Scaling reduction of port-Hamiltonian systems for numerical calculation

We present a novel reduction method of port-Hamiltonian systems by a renormalization group. The reduced system is suitable for a fast numerical calculation in a mesoscopic scale. Especially, we aim at the development of renormalized molecular dynamics with controls. First, we define a renormalized Hamiltonian with coarse graining. Next, we introduce a renormalized canonical Hamiltonian system. Moreover, we clarify the relationship between the renormalized Hamiltonian system and a Dirac structure. Finally, we obtain necessary conditions of boundary connections for each renormalized Hamiltonian system with different scales.