Neural Stream Function Method for Electrical Impedance Tomography with Lipschitz Conductivities
Abstract
Electrical impedance tomography (EIT) reconstructs the conductivity inside an object from voltage and current measurements on its boundary. The resulting inverse problem is nonlinear and severely ill-posed. Neural networks offer a flexible computational approach, but training physics informed neural networks for EIT and relating their training loss to reconstruction accuracy remain challenging. We develop a novel constrained neural stream function method for planar EIT with Lipschitz conductivities. The method builds the conductivity constraints and prescribed boundary voltages into the neural trial functions and replaces the second order conductivity equation with a first order system in strong form. The measured current is also used to construct a fixed baseline for the stream function. For this formulation, we derive error estimates that relate the sampled neural objective to errors in the physical boundary currents and the reconstructed conductivity. The error estimates separate the contributions from neural approximation, measurement noise, and sampling. Numerical experiments further demonstrate that the proposed method achieves high reconstruction accuracy with both exact and noisy boundary data.
Related
- At last, an explicit singular value decomposition for electrical impedance tomography
- A Self-Generated Local Structural Prior for Resolving Target Merging in Electrical Impedance Tomography (EIT)
- Determining W1,n conductivities in Calderón's problem for n≥4
- The conductivity problem with imperfect bonding interfaces and finite internal conductivities
- Fractional Calderón problem with L∞-conductivities
BibTeX
@misc{li2026neural,
title = {{Neural Stream Function Method for Electrical Impedance Tomography with Lipschitz Conductivities}},
author = {Xiaosheng Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38064},
eprint = {2610.38064},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38064},
}
RIS
TY - UNPB
TI - Neural Stream Function Method for Electrical Impedance Tomography with Lipschitz Conductivities
AU - Xiaosheng Li
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.38064
UR - https://arxiv.org/abs/2610.38064
AB - Electrical impedance tomography (EIT) reconstructs the conductivity inside an object from voltage and current measurements on its boundary. The resulting inverse problem is nonlinear and severely ill-posed. Neural networks offer a flexible computational approach, but training physics informed neural networks for EIT and relating their training loss to reconstruction accuracy remain challenging. We develop a novel constrained neural stream function method for planar EIT with Lipschitz conductivities. The method builds the conductivity constraints and prescribed boundary voltages into the neural trial functions and replaces the second order conductivity equation with a first order system in strong form. The measured current is also used to construct a fixed baseline for the stream function. For this formulation, we derive error estimates that relate the sampled neural objective to errors in the physical boundary currents and the reconstructed conductivity. The error estimates separate the contributions from neural approximation, measurement noise, and sampling. Numerical experiments further demonstrate that the proposed method achieves high reconstruction accuracy with both exact and noisy boundary data.
ER -