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Several reduced order models have been developed for nonlinear dynamicalsystems. To achieve a considerable speed-up, a hyper-reduction step is neededto reduce the computational complexity due to nonlinear terms. Manyhyper-reduction techniques require the construction of nonlinear term basis,which introduces a computationally expensive offline phase. A novel way ofconstructing nonlinear term basis within the hyper-reduction process isintroduced. In contrast to the traditional hyper-reduction techniques where thecollection of nonlinear term snapshots is required, the SNS method avoidscollecting the nonlinear term snapshots. Instead, it uses the solutionsnapshots that are used for building a solution basis, which enables avoidingan extra data compression of nonlinear term snapshots. As a result, the SNSmethod provides a more efficient offline strategy than the traditional modelorder reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. TheSNS method is theoretically justified by the conforming subspace condition andthe subspace inclusion relation. It is useful for model order reduction oflarge-scale nonlinear dynamical problems to reduce the offline cost. It isespecially useful for ST-GNAT that has shown promising results, such as a goodaccuracy with a considerable online speed-up for hyperbolic problems in arecent paper by Choi and Carlberg in SISC 2019, because ST-GNAT involves anexpensive offline cost related to collecting nonlinear term snapshots.Numerical results support that the accuracy of the solution from the SNS methodis comparable to the traditional methods and a considerable speed-up (i.e., afactor of two to a hundred) is achieved in the offline phase.

SNS: A Solution-based Nonlinear Subspace method for time-dependent model order reduction