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Parametric time-dependent systems are of a crucial importance in modelingreal phenomena, often characterized by non-linear behaviors too. Thosesolutions are typically difficult to generalize in a sufficiently wideparameter space while counting on limited computational resources available. Assuch, we present a general two-stages deep learning framework able to performthat generalization with low computational effort in time. It consists in aseparated training of two pipe-lined predictive models. At first, a certainnumber of independent neural networks are trained with data-sets taken fromdifferent subsets of the parameter space. Successively, a second predictivemodel is specialized to properly combine the first-stage guesses and computethe right predictions. Promising results are obtained applying the framework toincompressible Navier-Stokes equations in a cavity (Rayleigh-Bernard cavity),obtaining a 97% reduction in the computational time comparing with itsnumerical resolution for a new value of the Grashof number.

A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problems