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 $20\%$.

本文介绍了 CDII-PINNs，这是一种在 Tikhonov 正则化框架下使用 PINNs 求解 CDII 的计算有效方法。该方法通过将正则化最小二乘输出功能与描述电导率和电压之间关系的基础微分方程相结合，构建了一种物理学知识损失函数。其中，代表电导率和电压的一对神经网络通过这个损失函数相互耦合，然后最小化损失函数即可得到一种重建。我们提供了严格的理论保证和误差分析，证明 CDII-PINNs 非常高效、准确且对噪声水平从 1% 到 20% 的范围内的噪声具有鲁棒性。