  This paper presents a structure-preserving model reduction approach
applicable to large-scale, nonlinear port-Hamiltonian systems. Structure
preservation in the reduction step ensures the retention of port-Hamiltonian
structure which, in turn, assures the stability and passivity of the reduced
model. Our analysis provides a priori error bounds for both state variables and
outputs. Three techniques are considered for constructing bases needed for the
reduction: one that utilizes proper orthogonal decompositions; one that
utilizes $\mathcal{H}_2/\mathcal{H}_{\infty}$-derived optimized bases; and one
that is a mixture of the two. The complexity of evaluating the reduced
nonlinear term is managed efficiently using a modification of the discrete
empirical interpolation method (DEIM) that also preserves port-Hamiltonian
structure. The efficiency and accuracy of this model reduction framework are
illustrated with two examples: a nonlinear ladder network and a tethered Toda
lattice.
