the proper orthogonal decomposition for reduced order modelling at the example of the heat equa- tion, which is a prototypical example of a parabolic problem. The finite element . MODEL REDUCTION USING POD 5 is given by the singular vectors {ui}ℓ i=1, i.e., by the first ℓ columns of er, () argmax(Pℓ) = Xℓ i=1 σ2 i= Xℓ i=1 λ. Proof. Since (Pℓ) is an . particular, with respect linear-quadratic optimal control problems. Proper orthogonal decomposition (POD) isapowerfultechniqueformodel reductionofnon