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 $20\%$.

翻译：本文提出了一种名为CDII-PINNs的高效计算方法，该方法在Tikhonov正则化框架下利用物理信息神经网络求解CDII问题。该方法通过将正则化最小二乘输出泛函与描述电导率与电压关系的底层微分方程相融合，构造了物理信息损失函数。由一对分别表示电导率和电压的神经网络通过该损失函数耦合而成。随后，最小化损失函数即可实现重建。我们提供了严格的理论保证，给出了CDII-PINNs的误差分析，并基于预先选择的神经网络参数建立了关于样本数量的收敛速率。数值模拟表明，CDII-PINNs在处理$1\%$至$20\%$噪声水平时具备高效性、准确性和鲁棒性。