Author

Ran Ding

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#machine learning Preprint Sep 2026

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 whi...

Pei-Yao Chen, Zhou-Yuan Xu, Ran Ding et al. · 0 citations