{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T17:54:28Z","timestamp":1790186068843,"version":"4.1.0"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or with dissipation and hence plays a crucial role in the description of the physical properties of the system. Traditional hyper-reduction of nonlinear gradient fields yields efficient approximations that, however, lack the gradient structure. We focus on Hamiltonian gradients and propose to first decompose the nonlinear part of the Hamiltonian, mapped into a suitable reduced space, into the sum of [Formula: see text] terms, each characterized by a sparse dependence on the system state. Then the hyper-reduced approximation is obtained via discrete empirical interpolation (DEIM) of the Jacobian of the derived [Formula: see text]-valued nonlinear function. The resulting hyper-reduced model retains the gradient structure, and its computationally complexity is independent of the size of the full model. Moreover, a priori error estimates show that the hyper-reduced model converges to the reduced model and the Hamiltonian is asymptotically preserved. Whenever the evolution of the nonlinear Hamiltonian gradient requires high-dimensional DEIM approximation spaces, an adaptive strategy is performed. This consists in updating the hyper-reduced Hamiltonian via a low-rank correction of the DEIM basis. Numerical tests demonstrate the runtime speedups compared to the full and the reduced models.<\/jats:p>","DOI":"10.1137\/22m1503890","type":"journal-article","created":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T04:24:53Z","timestamp":1698207893000},"page":"A2725-A2754","source":"Crossref","is-referenced-by-count":22,"title":["Gradient-Preserving Hyper-Reduction of Nonlinear Dynamical Systems via Discrete Empirical Interpolation"],"prefix":"10.1137","volume":"45","author":[{"given":"Cecilia","family":"Pagliantini","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 di Pisa, Italy."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Federico","family":"Vismara","sequence":"additional","affiliation":[{"name":"Centre for Analysis, Scientific Computing and Applications, Eindhoven University of Technology, The Netherlands."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,10,25]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1137\/17M1111991"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.08.006"},{"key":"ref3","doi-asserted-by":"crossref","DOI":"10.3390\/mca24020043","volume":"24","author":"Buchfink P.","year":"2019","journal-title":"Math. 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Rave, PSD-Greedy basis generation for structure-preserving model order reduction of Hamiltonian systems, in Proceedings of the Conference Algoritmy, 2020, pp. 151\u2013160."},{"key":"ref5","series-title":"Lecture Notes in Math. 1764","volume-title":"Lectures on Symplectic Geometry","author":"Cannas da Silva A.","year":"2001"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/140959602"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.06.022"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1137\/15M1055085"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/090766498"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/110822724"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/15M1019271"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1002\/nme.4820"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2016.11.016"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.2307\/1967124"},{"key":"ref15","series-title":"Springer Ser. 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Wang, Structure-Preserving Galerkin POD-DEIM Reduced-Order Modeling of Hamiltonian Systems, https:\/\/arxiv.org\/abs\/2103.00388, 2021."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1503890","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:46:52Z","timestamp":1787327212000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1503890"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,25]]},"references-count":30,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10,31]]}},"alternative-id":["10.1137\/22M1503890"],"URL":"https:\/\/doi.org\/10.1137\/22m1503890","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,25]]}}}