Beyond Arbitrary Geometry: Topology Generalization In neural PDE Operators
Neural operators that accept arbitrary meshes are often treated as geometry-general, but unseen domain topology changes both the invariant and decaying subspaces of a PDE operator. We use Hodge heat flow as a controlled lens on this distinction and introduce TopoBox-3D, where tunnels and cavities vary Betti support while the exact Hodge decomposition separates the harmonic kernel from the positive spectrum. Across six architectures, models that infer topology implicitly suffer excess matched degradation in 37 of 45 model--task topology-OOD cells, yet cases that change harmonic dimension are not more strongly penalized on average. The dominant difficulty is instead spectral: the initial Ra...
| Authors | Peiyao Chen, Zhouyuan Xu, Ran Ding et al. |
|---|---|
| Primary category | cs.LG |
| Published | 5 September 2026 |
| Last updated at source | 13 September 2026 |
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- cppyyy/TopoBox-3DDataset · cited by
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- cppyyy/TopoBox-3DDataset
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