Grid-pretrained physics models move onto unstructured meshes: swap the outer convolution, and cylinder flow runs zero-shot below most trained baselines

The tokenisation layer of a physics foundation model can now act on unstructured meshes instead of switching to a graph neural network. Such models previously relied on convolutional encoders over regular grids, while unstructured mesh data went to graph neural networks, which encode information differently and block weight portability between the two regimes. On the turbulent radiative layer, shear flow and active matter datasets from The Well, loading grid-pretrained weights directly into the mesh-native convolutional encoder beats all mesh baselines trained from scratch on both next-step and ten-step rollout metrics in zero-shot transfer.

The construction extends the discrete convolution kernel into a continuous kernel and aggregates information over mesh nodes inside a geometric window. Mesh-native convolution interpolates the discrete kernel into a continuous spline kernel, so the window position and kernel spacing follow physical coordinates rather than graph hops. On the points of a regular grid the layer equals the classical convolutional layer node by node, which is what allows pretrained convolutional weights to be loaded by name; on unstructured meshes an occupancy normalisation compensates for uneven sampling density.

The same layer attaches to a large multi-physics foundation model and handles a flow configuration absent from its pretraining corpus. The cylinder-flow data are not part of that foundation model's pretraining corpus, so the model has no prior knowledge of this flow configuration. On the MeshGraphNets cylinder-flow benchmark, the model with its outermost convolutions replaced has lower zero-shot error than every trained baseline except Transolver++, and the lowest next-step error after fine-tuning; each configuration used the same 7.5-hour budget on a single GH200.

The method targets continuum simulation on unstructured meshes, for researchers and engineers training physics surrogates. The demonstrated scope covers three two-dimensional datasets from The Well and the MeshGraphNets cylinder-flow benchmark, where the meshes were uniformly refined three times to match pretraining resolution and all scores were computed on the original mesh nodes. The source proposes future work on geometric quadrature weights for varying sampling density, and on using retrofitted emulators as initial guesses for implicit time stepping.

The source states that mesh-native retrofitting mainly improves sample efficiency, speeding up fine-tuning rather than raising final accuracy after sufficient training, so the benefit is largest when training data or compute are limited. Cross-physics controls show that GINO has lower zero-shot errors from either individual source, that mixed-source pretraining is what substantially improves this method's initialisation, and that its pretraining gain over its own scratch run is modest, so the result should not be generalised to arbitrary cross-physics initialisation or to forecasting.