Canonical and Noncanonical Hamiltonian Operator Inference
This work addresses the challenge of efficiently simulating complex Hamiltonian systems in fields like physics and engineering, representing an incremental improvement by adapting operator inference to preserve structure.
The paper tackles the problem of model reduction for Hamiltonian systems by introducing a nonintrusive, structure-preserving method based on operator inference, which is provably convergent and yields accurate, stable reduced models that preserve conserved quantities beyond training data.
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a straightforward linear solve given snapshot data and gray-box knowledge of the system Hamiltonian. Examples involving several hyperbolic partial differential equations show that the proposed method yields reduced models which, in addition to being accurate and stable with respect to the addition of basis modes, preserve conserved quantities well outside the range of their training data.