计算电磁学主要研究基于计算机技术数值求解麦克斯韦方程组的方法与相关技术，是电磁场相关领域中理论研究和工程应用的科学工具。计算效率一直是电磁计算方法研究的重点之一，传统的加速方法一般是从电磁场数学模型出发，包括通过优化物理规律计算的加速方法以及基于线下预计算的加速方法。 近年来，随着大数据技术和高性能计算平台的性能不断发展，大规模多层深度神经网络并行优化计算变得容易，使得深度学习技术迅速发展，在图像、音频、视频领域获得了广泛地应用。此外，深度学习通过融合数据、物理先验和数学方法，并基于GPU并行计算平台，推动了物理、应用数学和工程领域中快速算法的发展。本文针对深度学习在电磁快速计算方法中的应用进行了深入探索与研究。 本文研究了数据驱动的深度学习电磁仿真方法，求解单物理量和多物理量电磁问题，包括求解二维和三维泊松方程，大地电磁建模和反射阵相位综合。主要研究在不同类型电磁问题中，深度卷积神经网络结构设计，神经网络模型的目标函数、评价函数和正则化函数设计，网络模型优化等技术。数值算例表明数据驱动的深度学习电磁仿真方法可以在保证两位数值精度的同时，获得一到两个量级的加速。 面向相控电磁表面实时波束操控应用场景，本文提出了基于深度学习技术的智能编码方法。基于数据驱动的深度学习方法从数据中学习并掌握波束参数与编码之间的物理规律，实现多波束毫秒级操控，该方法分别在1600单元和2304单元1bit相控电磁表面上实现了多波束扫描，并通过微波暗室的测试结果验证了该方法的有效性和鲁棒性。 本文研究了物理驱动的深度学习电磁快速计算方法，将电磁计算方法与深度学习相结合，提出了融合物理的监督残差学习方法，为求解电磁正问题和逆散射问题提供了通用框架。该方法基于深度神经网络实现线性方程组的定常和非定常迭代算法数学过程，提升了迭代算法的收敛速度，通过求解体积分方程验证了该方法的通用性和泛化能力。进一步，将电磁逆散射问题的波恩迭代方法与融合物理的监督残差学习方法相结合，求解二维电磁逆散射问题，数值算例验证了方法的有效性。

Computational electromagnetics (CEM) mainly studies numerical algorithms of solving Maxwell’s equations based on modern computer science. CEM is an important scientific tool for theoretical research and applications of engineering in the electromagnetics and related fields. Computing efficiency has always been one of cores in the research of electromagnetic computational methods. Traditional methods to improve the computing efficiency are based on mathematical models of electromagnetics including acceleration by reducing the computational complexity of physical laws and acceleration based on the offline pre-calculation. Recently, the rapid development of the big data technology and high-performance computing platforms makes it easy to train and optimize large-scale multi-layer deep neural networks in parallel, and deep learning is ushering in leapfrog developments and has gained widespread applications in the image, speech, and video fields. Additionally, with the parallel platform GPU, deep learning promotes the development of fast computational methods in the fields of physics, applied mathematics and engineering by fusing big data, physical priors and mathematical methods. This thesis conducts in-depth exploration and study on the applications of deep learning in fast electromagnetic computational methods. This thesis studies the data-driven deep learning electromagnetic simulation methods, which are applied into electromagnetic problems with single physical quantity and multiple physical quantities, including solving two-dimensional and three-dimensional Poisson’s equations, forward modeling in magnetotellurics and phase synthesis of reflectarrays. The approaches are studied to design the structure, objective function, evaluation function, regularization and optimization of deep convolutional neural networks in various types of electromagnetic problems. Numerical results show that the data-driven deep learning electromagnetic simulation methods can speed up computation by one to two orders with two-digit numerical precision. For the application scenario of real-time beam steering on the phased electromagnetic surface, this thesis proposes an intelligent coding scheme based on deep learning techniques. The data-driven deep learning method can learn and master the inner physical laws between the beam parameters and codes from the data set, then realize the manipulation of multi-beams in milliseconds. The proposed approach is implemented to achieve multiple beam steering on the 1600-element and 2304-element 1bit phased electromagnetic surfaces. The validity and robustness are verified by the measurements in a microwave anechoic chamber. This thesis studies the physics-informed deep learning fast computational electromagnetic methods and proposes the physics-informed supervised residual learning method by incorporating computational electromagnetic methods with deep learning, which provides a general framework for solving electromagnetic forward modeling and inverse scattering problems. This method realizes the mathematical process of the stationary and non-stationary iterative algorithms for solving linear equations, which speeds up the convergence rate of the iterative algorithms. The versatility and generalization ability are verified by solving volume integral equations. Furthermore, the Born iterative method is incorporated into the physics-informed supervised residual learning method to solve the two-dimensional inverse scattering problems, and the effectiveness is verified by numerical examples.