  This paper presents a structure-exploiting nonlinear model reduction method
for systems with general nonlinearities. First, the nonlinear model is lifted
to a model with more structure via variable transformations and the
introduction of auxiliary variables. The lifted model is equivalent to the
original model---it uses a change of variables, but introduces no
approximations. When discretized, the lifted model yields a polynomial system
of either ordinary differential equations or differential algebraic equations,
depending on the problem and lifting transformation. Proper orthogonal
decomposition (POD) is applied to the lifted models, yielding a reduced-order
model for which all reduced-order operators can be pre-computed. Thus, a key
benefit of the approach is that there is no need for additional approximations
of nonlinear terms, in contrast with existing nonlinear model reduction methods
requiring sparse sampling or hyper-reduction. Application of the lifting and
POD model reduction to the FitzHugh-Nagumo benchmark problem and to a tubular
reactor model with Arrhenius reaction terms shows that the approach is
competitive in terms of reduced model accuracy with state-of-the-art model
reduction via POD and discrete empirical interpolation, while having the added
benefits of opening new pathways for rigorous analysis and input-independent
model reduction via the introduction of the lifted problem structure.
