Reduced-order models for parametric problems are confronted to the necessity of generating a set of snapshots able of configuring a representative basis of the solution manifold. Both in standard reduced-basis approaches or in POD with Galerkin projection, producing snapshots is one of the most time-consuming processes. Browsing the parametric space and computing the full-order solution for many parametric values is often unaffordable. In nonlinear reduced-order modelling via the kPOD concept [1], it is necessary to locally enrich the local basis in order to ease the backward mapping. In this framework, data augmentation consists in computing a low number of full-order solutions and generate from them many others likely corresponding to intermediate values of the parameters. Different ideas on how to generate these artificial snapshots for different problems are discussed, some based in physical rationales, others purely geometric. Note that in this context physics are always enforced due to the a posteriori character of the reduced-order model: even if the new snapshot is non-physical, it may bring to the enriched basis emerging features of the solution in the new parametric values. This is discussed in detail in [2], where these ideas are applied to steady-state Navier-Stokes problems. REFERENCES [1] Díez, P.; Muixí, A.; Zlotnik, S.; García-González, A.; "Nonlinear dimensionality reduction for parametric problems: a kernel Proper Orthogonal Decomposition (kPOD)", International Journal for Numerical Methods in Engineering, 122 (24) 7306-7327 (2021) https://doi.org/10.1002/nme.6831 [2] Muixí, A.; Zlotnik, S.; Giacomini, M.; Díez, P.; “Data Augmentation for the POD Formulation of the Parametric Laminar Incompressible Navier–Stokes Equations”, International Journal for Numerical Methods in Engineering, 2025, 126(1) e7624 https://doi.org/10.1002/nme.7624