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A method for the nonintrusive and structure-preserving model reduction ofcanonical and noncanonical Hamiltonian systems is presented. Based on the ideaof operator inference, this technique is provably convergent and reduces to astraightforward linear solve given snapshot data and gray-box knowledge of thesystem Hamiltonian. Examples involving several hyperbolic partial differentialequations show that the proposed method yields reduced models which, inaddition to being accurate and stable with respect to the addition of basismodes, preserve conserved quantities well outside the range of their trainingdata.

Canonical and Noncanonical Hamiltonian Operator Inference