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Rapid simulations of advection-dominated problems are vital for multipleengineering and geophysical applications. In this paper, we present a longshort-term memory neural network to approximate the nonlinear component of thereduced-order model (ROM) of an advection-dominated partial differentialequation. This is motivated by the fact that the nonlinear term is the mostexpensive component of a successful ROM. For our approach, we utilize aGalerkin projection to isolate the linear and the transient components of thedynamical system and then use discrete empirical interpolation to generatetraining data for supervised learning. We note that the numericaltime-advancement and linear-term computation of the system ensure a greaterpreservation of physics than does a process that is fully modeled. Our resultsshow that the proposed framework recovers transient dynamics accurately withoutnonlinear term computations in full-order space and represents a cost-effectivealternative to solely equation-based ROMs.

Using recurrent neural networks for nonlinear component computation in advection-dominated reduced-order models