For real analytic F, exact uniqueness F(p)=F(q) implies R(p)=R(q) yields Hölder stability of R on compact subsets of the parameter domain.
Global uniqueness for a two-dimensional inverse boundary value problem
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Symbolic rational-function networks recover an admissible PDE from noiseless complete measurements and select the regularization-minimizing parameterization within the architecture.
Asymptotic expansions are derived for a solid Cauchy transform of a rapidly oscillating phase when a stationary point approaches the Cauchy singularity within O(sqrt(h)), using polarization in C^2 and Stokes' theorem.
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.
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H\"older Stability from Exact Uniqueness for Finite-Dimensional Analytic Inverse Problems
For real analytic F, exact uniqueness F(p)=F(q) implies R(p)=R(q) yields Hölder stability of R on compact subsets of the parameter domain.
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Symbolic recovery of PDEs from measurement data
Symbolic rational-function networks recover an admissible PDE from noiseless complete measurements and select the regularization-minimizing parameterization within the architecture.
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Stationary phase with Cauchy singularity. A critical point of signature $(+,-)$
Asymptotic expansions are derived for a solid Cauchy transform of a rapidly oscillating phase when a stationary point approaches the Cauchy singularity within O(sqrt(h)), using polarization in C^2 and Stokes' theorem.
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A DeepONet for inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An approximation theoretic perspective and numerical results
DeepONet learns the operator-to-function map from N-t-D data to conductivities in EIT, supported by a universal approximation theorem and numerical outperformance of IRGN.