Current density impedance imaging with PINNs

TL;DR

This paper presents CDII-PINNs, a physics-informed neural network approach for efficient and accurate electrical impedance imaging, with theoretical guarantees and robustness to noise.

Contribution

The paper introduces a novel PINN-based method for CDII with theoretical error analysis and convergence guarantees, improving computational efficiency and robustness.

Findings

Efficient and accurate reconstructions demonstrated in simulations.

Method robust to noise levels up to 20%.

Provides theoretical error bounds and convergence rates.

Abstract

In this paper, we introduce CDII-PINNs, a computationally efficient method for solving CDII using PINNs in the framework of Tikhonov regularization. This method constructs a physics-informed loss function by merging the regularized least-squares output functional with an underlying differential equation, which describes the relationship between the conductivity and voltage. A pair of neural networks representing the conductivity and voltage, respectively, are coupled by this loss function. Then, minimizing the loss function provides a reconstruction. A rigorous theoretical guarantee is provided. We give an error analysis for CDII-PINNs and establish a convergence rate, based on prior selected neural network parameters in terms of the number of samples. The numerical simulations demonstrate that CDII-PINNs are efficient, accurate and robust to noise levels ranging from $1\%$ to $20\%$.