Cellular Sheaf Neural Operators

Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs

arXiv:2606.00937v1 Announce Type: cross Abstract: Neural operators provide fast surrogate models for PDE simulations, but standard architectures often treat geometry and discretization as secondary to field data. Physical states are usually represented as grid-channel stacks, even when different quantities naturally belong on vertices, edges, faces, cells, boundaries, or interfaces and must satisfy compatibility constraints. We propose Cellular Sheaf Neural Operators, a discretization-aware...