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.
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Regularization of Fourier multipliers yields L^∞ stability for wave propagation and compact operator inversion in inverse problems.
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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.
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On $L^\infty$ stability for wave propagation and for linear inverse problems
Regularization of Fourier multipliers yields L^∞ stability for wave propagation and compact operator inversion in inverse problems.