# Extension and neural operator approximation of the electrical impedance tomography inverse map

arXiv: https://arxiv.org/abs/2511.20361 · HTML: https://mlsanity.com/paper/2511.20361/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2025.

## Built on by (most cited first, 3 of 3)

- [A short tour of operator learning theory: Convergence rates, statistical limits, and open questions](https://mlsanity.com/paper/2603.00819/) (2026)
- [One Operator for Many Densities: Amortized Approximation of Conditioning by Neural Operators](https://mlsanity.com/paper/2605.06873/) (2026)
- [Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects](https://mlsanity.com/paper/2605.16966/) (2026)

## Abstract (arXiv)

This paper considers the problem of noise-robust neural operator approximation for the solution map of Calder'on's inverse conductivity problem. In this continuum model of electrical impedance tomography (EIT), the boundary measurements are realized as a noisy perturbation of the Neumann-to-Dirichlet map's integral kernel. The theoretical analysis proceeds by extending the domain of the inversion operator to a Hilbert space of kernel functions. The resulting extension shares the same stability properties as the original inverse map from kernels to conductivities, but is now amenable to neural operator approximation. Numerical experiments demonstrate that Fourier neural operators excel at reconstructing infinite-dimensional piecewise constant and lognormal conductivities in noisy setups both within and beyond the theory's assumptions. The methodology developed in this paper for EIT exemplifies a broader strategy for addressing nonlinear inverse problems with a noise-aware operator learning framework.