Tikhonov regularization is analyzed using neural operators as learned surrogates for ill-posed nonlinear operator equations, with error balancing and approximation results extended to Sobolev and Lebesgue spaces.
Behavior of the error of the approximate solutions of boundary value problems for linear elliptic operators by Galerkin’s and finite difference methods
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Neural operators for solving nonlinear inverse problems
Tikhonov regularization is analyzed using neural operators as learned surrogates for ill-posed nonlinear operator equations, with error balancing and approximation results extended to Sobolev and Lebesgue spaces.