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When learning simulations for modeling physical phenomena in industrialdesigns, geometrical variabilities are of prime interest. While classicalregression techniques prove effective for parameterized geometries, practicalscenarios often involve the absence of shape parametrization during theinference stage, leaving us with only mesh discretizations as available data.Learning simulations from such mesh-based representations poses significantchallenges, with recent advances relying heavily on deep graph neural networksto overcome the limitations of conventional machine learning approaches.Despite their promising results, graph neural networks exhibit certaindrawbacks, including their dependency on extensive datasets and limitations inproviding built-in predictive uncertainties or handling large meshes. In thiswork, we propose a machine learning method that do not rely on graph neuralnetworks. Complex geometrical shapes and variations with fixed topology aredealt with using well-known mesh morphing onto a common support, combined withclassical dimensionality reduction techniques and Gaussian processes. Theproposed methodology can easily deal with large meshes without the need forexplicit shape parameterization and provides crucial predictive uncertainties,which are essential for informed decision-making. In the considered numericalexperiments, the proposed method is competitive with respect to existing graphneural networks, regarding training efficiency and accuracy of the predictions.

MMGP: a Mesh Morphing Gaussian Process-based machine learning method for  regression of physical problems under non-parameterized geometrical  variability