Solving the combined field integral equation (CFIE) for the large-scale scattering problem is computationally expensive. In this letter, we investigate the feasibility of applying deep learning to solve the CFIE for 2-D perfect electrically conducting objects. Inspired by the conjugate gradient method, an iterative deep neural network is designed to learn the manner of solving the surface current density from the CFIE, with the input being the coefficient matrix of the equation. This process involves physics through surface integration and need less iterations than the conventional iterative equation solver. In numerical tests, we evaluate the network's performance by comparing the predicted surface current density and bistatic scattering cross section with the solutions rigorously computed. This method provides an insight into applying machine learning techniques together with electromagnetic (EM) physics to fast EM computation with the same level of accuracy as traditional method.

中文翻译：

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用深度神经网络求解二维导电物体的组合场积分方程。

解决大规模散射问题的组合场积分方程（CFIE）在计算上是昂贵的。在这封信中，我们研究了应用深度学习解决二维完美导电物体的CFIE的可行性。受共轭梯度法的启发，设计了一个迭代式深度神经网络，以从CFIE中学习求解表面电流密度的方式，输入是方程的系数矩阵。该过程涉及通过表面积分的物理过程，比常规的迭代方程求解器需要更少的迭代。在数值测试中，我们通过将预测的表面电流密度和双基地散射截面与严格计算的解决方案进行比较，来评估网络的性能。