Here, 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.
Gruber, Anthony David and Tezaur, Irina Kalashnikova. "Canonical and noncanonical Hamiltonian operator inference." Computer Methods in Applied Mechanics and Engineering, vol. 416, Aug. 2023. https://doi.org/10.1016/j.cma.2023.116334
Gruber, Anthony David, and Tezaur, Irina Kalashnikova, "Canonical and noncanonical Hamiltonian operator inference," Computer Methods in Applied Mechanics and Engineering 416 (2023), https://doi.org/10.1016/j.cma.2023.116334
@article{osti_2311488,
author = {Gruber, Anthony David and Tezaur, Irina Kalashnikova},
title = {Canonical and noncanonical Hamiltonian operator inference},
annote = {Here, 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.},
doi = {10.1016/j.cma.2023.116334},
url = {https://www.osti.gov/biblio/2311488},
journal = {Computer Methods in Applied Mechanics and Engineering},
issn = {ISSN 0045-7825},
volume = {416},
place = {United States},
publisher = {Elsevier},
year = {2023},
month = {08}}
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conferencehttps://doi.org/10.1109/CDC.2009.5400045