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This work introduces a novel approach for data-driven model reduction oftime-dependent parametric partial differential equations. Using a multi-stepprocedure consisting of proper orthogonal decomposition, dynamic modedecomposition and manifold interpolation, the proposed approach allows toaccurately recover field solutions from a few large-scale simulations.Numerical experiments for the Rayleigh-B\'{e}nard cavity problem show theeffectiveness of such multi-step procedure in two parametric regimes,i.e.~medium and high Grashof number. The latter regime is particularlychallenging as it nears the onset of turbulent and chaotic behaviour. A majoradvantage of the proposed method in the context of time-periodic solutions isthe ability to recover frequencies that are not present in the sampled data.

A Data-Driven Surrogate Modeling Approach for Time-Dependent  Incompressible Navier-Stokes Equations with Dynamic Mode Decomposition and  Manifold Interpolation