Canonical and noncanonical Hamiltonian operator inference. (English) Zbl 1536.65164
Summary: 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.
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 65M22 | Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
digital twin (DT); projection-based model order reduction (PMOR); Hamiltonian systems; operator inference; structure preservation; proper orthogonal decomposition (POD)References:
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