GAIA introduces a geometry-adaptive integral autoencoder that unifies forward, boundary-value, and inverse PDE operator learning on arbitrary domains via geometry tokens and cross-attention.
arXiv:2511.01924 (NeurIPS 2025)
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Hybrid exact-learned equivariant operator for incompressible Stokes flow fixes the known core kernel exactly and learns only the boundary correction as a second-kind operator, achieving high accuracy, data efficiency, and cross-shape generalization.
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Solver Exactness, Learned Flexibility: Equivariant Boundary-Correction Operators for Stokes Flow
Hybrid exact-learned equivariant operator for incompressible Stokes flow fixes the known core kernel exactly and learns only the boundary correction as a second-kind operator, achieving high accuracy, data efficiency, and cross-shape generalization.