Current density impedance imaging with PINNs
This work addresses computational efficiency and accuracy in medical or material imaging, but it appears incremental as it applies an existing PINN framework to a specific imaging problem.
The paper tackles the problem of current density impedance imaging (CDII) by proposing CDII-PINNs, a method that uses physics-informed neural networks (PINNs) with Tikhonov regularization to reconstruct conductivity and voltage, achieving efficient and accurate results with robustness to noise levels from 1% to 20%.
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 $20\%$.