Surrogate models for steady partial differential equations on unstructured meshes typically apply a single mixing mechanism to the whole solution. This can be limiting when different regions of the domain exhibit different behaviors, especially on coarse meshes where resolution is already scarce.
The paper proposes an architecture that partitions the solution among multiple experts, guided by a learnable Hodge-Laplacian operator. This design allows different experts to specialize in different parts of the solution, potentially improving fidelity compared to a one-size-fits-all mixing scheme.
The abstract outlines the motivation and the proposed architecture but does not yet include experimental results. Still, the idea points to a promising direction for mesh-based PDE surrogates, where adaptive partitioning could help capture localized dynamics more efficiently.