A deformation-based metric framework lets neural operators learn PDE solution maps on non-diffeomorphic, varying domains, with a convergence proof for Poisson on star domains and a D2E variant that avoids deformation-related regularity artifacts.
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A deformation-based framework for learning solution mappings of PDEs defined on varying domains
A deformation-based metric framework lets neural operators learn PDE solution maps on non-diffeomorphic, varying domains, with a convergence proof for Poisson on star domains and a D2E variant that avoids deformation-related regularity artifacts.