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In this work, the dual-weighted residual (DWR) method is applied to obtain acertified incremental proper orthogonal decomposition (POD) based reduced ordermodel. A novel approach called MORe DWR (Model Order Rduction withDual-Weighted Residual error estimates) is being introduced. It marriestensor-product space-time reduced-order modeling with time slabbing and anincremental POD basis generation with goal-oriented error control based ondual-weighted residual estimates. The error in the goal functional is beingestimated during the simulation and the POD basis is being updated if theestimate exceeds a given threshold. This allows an adaptive enrichment of thePOD basis in case of unforeseen changes in the solution behavior which is ofhigh interest in many real-world applications. Consequently, the offline phasecan be skipped, the reduced-order model is being solved directly with the PODbasis extracted from the solution on the first time slab and -- if necessary --the POD basis is being enriched on-the-fly during the simulation withhigh-fidelity finite element solutions. Therefore, the full-order model solvescan be reduced to a minimum, which is demonstrated on numerical tests for theheat equation and elastodynamics.

MORe DWR: Space-time goal-oriented error control for incremental POD-based ROM