Current density impedance imaging with PINNs
Chenguang Duan Yuling Jiao Xiliang Lu Jerry Zhijian Yang
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 $20\%$.