CEGINO: CONTINUOUS EQUIVARIANT GEOMETRY- INFORMED NEURAL OPERATORS FOR 3D PDES

Neural operators offer fast surrogates for partial differential equations on irregular 3D geometries, but coordinate-dependent representations can make their predictions sensitive to changes in reference frame. EqGINO addresses this issue through equivariant Fourier operators, yet its exact rotational equivariance is restricted to grid-compatible rotations. This limitation motivates representations that can support rotational robustness beyond a discrete symmetry group without relying on a Cartesian latent grid. To this end, we introduce CEGINO, a compact geometry-informed neural operator for surface-field prediction. CEGINO encodes geometry through rotation-invariant descriptors, propagates features over sparse anchors, and reconstructs physical fields through two-scale query decoding. Global context complements local propagation, with invariant anchor attention included in the matched pressure configuration. Scalar outputs use invariant decoding, while wall-shear-stress vectors are reconstructed in a rotation-consistent local basis. We evaluate the framework on AhmedBody, ShapeNetCar, and DeepJEB, and conduct a controlled three-seed comparison with EqGINO on AhmedBody pressure to examine the resulting accuracy–robustness trade-off. EqGINO achieves higher accuracy in canonical and grid-compatible orientations, whereas CEGINO better preserves predictive performance under the tested unseen non-grid rotations without rotation augmentation, while requiring fewer parameters, lower forward-pass latency, and less memory. These findings support sparse invariant representations as a practical approach to balancing rotational robustness and computational efficiency in surface-field surrogate modeling. Code is available at https://anonymous.4open.science/r/CEGINO-9756.