Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.
Hyman, Mimetic finite difference methods for maxwell’s equations and the equations of magnetic diffusion, Progress In Electromagnetics Research 32 (2000)
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Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs
Cellular Sheaf Neural Operators use cell complexes, learned restriction maps, and structure-aware message passing to create discretization-aware neural surrogates that preserve constraints in multiphysics PDEs such as MHD.