Neural and spectral operators can approximate shape-to-solution maps for families of elliptic and parabolic PDEs and BIEs with provable uniform error bounds derived from parametric holomorphy on a reference domain.
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Minimum number of terms for exact antisymmetry in a class of TPFs grows exponentially with dimension, shown via CP rank of antisymmetric tensors.
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Neural Shape Operator Surrogates -- Expression Rate Bounds
Neural and spectral operators can approximate shape-to-solution maps for families of elliptic and parabolic PDEs and BIEs with provable uniform error bounds derived from parametric holomorphy on a reference domain.
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Lower Bound on the Representation Complexity of Antisymmetric Tensor Product Functions
Minimum number of terms for exact antisymmetry in a class of TPFs grows exponentially with dimension, shown via CP rank of antisymmetric tensors.