Proves the first universal approximation theorems for k-times differentiable nonlinear operators between Banach spaces and their derivatives uniformly on compact sets in weighted Sobolev norms via encoder-decoder operator learning architectures.
Elsevier, 2003
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
years
2026 2verdicts
UNVERDICTED 2representative citing papers
A first-order semi-implicit finite element method for nonlinear poroelastic flow is shown to have unique solutions and to converge at optimal rates when the nonlinear strain-stress perturbation is sufficiently small.
citing papers explorer
-
Universal Approximation of Nonlinear Operators and Their Derivatives
Proves the first universal approximation theorems for k-times differentiable nonlinear operators between Banach spaces and their derivatives uniformly on compact sets in weighted Sobolev norms via encoder-decoder operator learning architectures.
-
Error analysis for the approximation of a flow in deformable porous media with nonlinear strain-stress relation
A first-order semi-implicit finite element method for nonlinear poroelastic flow is shown to have unique solutions and to converge at optimal rates when the nonlinear strain-stress perturbation is sufficiently small.