Mesh-native convolutions for retrofitting grid-pretrained physics models to unstructured meshes

Pretrained physics emulators are increasingly used as fast but imperfect substitutes for scientific simulators, and one of their imperfections is representational: trained on idealised simulation corpora often posed on regular grids, they cannot be confronted with the data of many applications, where fields live on unstructured meshes over irregular geometries. The mismatch is localised in a thin layer, the convolutional encoder/decoder pairs (tokenisers) that lift fields into and out of the latent space are tied to the grid, while the graph-based alternatives used for unstructured data are more expensive to train and encode information differently, so the simulator-trained prior cannot be reused. In this work we introduce Mesh-Native Convolution (MNC), a locality-aware tokenisation layer that operates on arbitrary point sets and reduces \emph{exactly} to strided convolution on regular grids. On fluid-dynamics benchmarks (the Well; MeshGraphNets cylinder flow), grid-pretrained weights loaded into MNC reconstruct fields on irregular meshes to high accuracy in zero-shot mode and reach convergence within a few epochs, offering a cheap route for carrying simulator-trained priors to unstructured scientific data.