Coordinates Are Labels, Not Physics: Breaking the Coordinate Shortcut in Neural Surrogates

Neural surrogates approximate physical fields at a lower computational cost than numerical simulation. On aligned vehicle benchmarks, a shared pose and fixed inflow direction allow models to predict field values from absolute coordinates, a strategy we call the coordinate shortcut. Low error on these benchmarks therefore does not show whether a model has learned how the field responds to geometry and boundary conditions. We evaluate surrogates beyond this setting, under unseen inflow directions and on geometries from unrelated shape families. Removing coordinate inputs prevents the shortcut but also discards spatial information about the arrangement of points within a geometry. We propose GraFINS (Graph-Encoded Frame-Invariant Neural Surrogate), which replaces coordinate inputs with frame-invariant features encoding local geometry and its relation to boundary conditions, and a graph embedding encoding spatial information. Trained only on vehicles with flow from the front, GraFINS predicts pressure under side and rear inflow more accurately than equivariant and non-equivariant baselines given the same features, and without retraining it also outperforms them on non-vehicle geometries. It preserves in-distribution accuracy on automotive and patient-specific blood-vessel benchmarks and remains stable under scene rotations.