Available dataset and code The code corresponding to the two-dimensional solid mechanics case (Tensile2d) described in Section 4.1 is available at https://gitlab.com/drti/mmgp Details regarding the datasets are provided in Appendix A. Morphing strategies and dimensionality reduction techniques are described in Appendices B and C. Details about the GNNs baselines are given in Appendix D. Finally, additional results about the considered experiments are gathered in Appendix E. This section provides additional details regarding the synthetic datasetsTensile2d andRotor37. Regarding theAirfRANS dataset, the reader is referred to [14]. A.1 Rotor37 dataset Examples of input geometries are shown in Figure 6 together with the associated output pressure fields. While the geometrical variabilities are moderate, it can be seen that they have a significant impact on the output pressure field.