Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.
Shape derivative- informed neural operators with application to risk-averse shape optimization
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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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Universal Approximation of Nonlinear Operators and Their Derivatives
Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.
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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.