Surrogate-Based ℋ2 Model Reduction of Port-Hamiltonian Systems

Interpolatory methods for structure-preserving model reduction of port-Hamiltonian systems are especially suitable for very large-scale models, owing to their low computational cost and memory requirements. ${{\mathcal{H}}_2}$-based techniques iteratively search for models which fulfill a subset of first-order ${{\mathcal{H}}_2}$-optimality conditions. In each iteration, a new reduced-order model is computed, which might weaken the computational advantages in cases of slow convergence. We propose a new structure-preserving framework for port-Hamiltonian systems based on surrogate modeling. By exploiting the local nature of the ${{\mathcal{H}}_2}$-optimization problem, the cost of optimization is decoupled from the cost of reduction. Consequently, ${{\mathcal{H}}_2}$-based interpolatory methods can be accelerated significantly and especially for very large-scale port-Hamiltonian systems, which is illustrated by a numerical example.