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We formulate this inverse problem as an operator-learning task, where the aim is to approximate the implicitly defined map from N\u2013t\u2013D operators to admissible conductivities. To this end, we employ a Deep Operator Network (DeepONet) architecture, thereby extending operator learning beyond the classical function-to-function setting to the more challenging operator-to-function regime. We establish a universal approximation theorem that guarantees that such operator-to-function maps can be approximated arbitrarily well by DeepONets. Furthermore, we provide a computational implementation of our approach and compare it against the iteratively regularized Gauss\u2013Newton (IRGN) method. Our results show that the proposed framework yields accurate and robust reconstructions, outperforms the baseline, and demonstrates strong generalization. To our knowledge, this is the first work that combines rigorous approximation-theoretic guarantees with DeepONet-based inversion for EIT, thereby opening a principled and interpretable pathway for use of DeepONets in such inverse problems.<\/jats:p>","DOI":"10.1007\/s10915-026-03300-0","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T11:43:40Z","timestamp":1777895020000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A DeepONet for Inverting the Neumann-to-Dirichlet Operator in Electrical Impedance Tomography: An Approximation Theoretic Perspective and Numerical Results"],"prefix":"10.1007","volume":"107","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3440-130X","authenticated-orcid":false,"given":"Anuj","family":"Abhishek","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6712-2171","authenticated-orcid":false,"given":"Thilo","family":"Strauss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"issue":"2","key":"3300_CR1","doi-asserted-by":"publisher","first-page":"165","DOI":"10.4171\/msl\/14","volume":"2","author":"K Abraham","year":"2019","unstructured":"Abraham, K., Nickl, R.: On statistical Calder\u00f3n problems. 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