**Author:** Yu Fan
background
东南大学崔铁军院士团队近期发表了一篇“智能电磁计算的若干进展”的综述论文[1]，里面详尽地描述了人工智能在电磁计算领域的进展，为读者入门并了解该领域最新的研究成果提供有益帮助。昇思MindSpore[2]是最早提出电磁仿真套件的AI框架，本文将结合昇思MindSpore Elec电磁仿真套件[3]进行论文分析。论文从算法层面分别介绍了智能电磁计算在正向电磁仿真和逆向电磁成像上的最新研究成果，随后从软硬件或数字物理相结合的系统层面介绍了基于信息超材料的智能计算新体制和相关应用，最后对全文进行了总结并预测智能电磁计算的发展方向。本文主要围绕算法软件层面介绍。
**1. ** Forward intelligent electromagnetic simulation
Forward electromagnetic simulation technology plays a decisive role in electromagnetic compatibility analysis, electronic device design, signal processing, communication network design and other fields. Mastering independent and controllable accurate and fast forward electromagnetic simulation technology is an important indicator to measure a country's scientific and technological level and industrial manufacturing capabilities.
Forward electromagnetic simulation calculation methods mainly include full-wave simulation methods such as finite difference method, finite element method, and moment method, as well as high-frequency asymptotic methods such as bouncing ray method. However, in the face of real-time, multi-scale and other requirements, there is still a long way to go. Therefore, a new computing paradigm needs to be proposed to solve the computational efficiency problems faced by traditional methods. Intelligent computing can improve forward simulation efficiency. Its essence is to extract effective physical information by learning the mapping relationship from input to output, thereby constructing an equivalent neural network model to replace traditional numerical operators, while ensuring that the calculation accuracy remains basically unchanged. Computational complexity reduction. Forward intelligent electromagnetic computing is mainly divided into two categories: data-driven and physical-driven. Intelligence is regarded as one of the most important future development directions in the field of computational electromagnetics.
1.1****Data-driven forward electromagnetic calculation
Data-driven electromagnetic calculations are roughly divided into result learning (that is, directly learning the mapping from electromagnetic parameters to expected calculation results, including field values and currents, etc.) and process learning (that is, using neural networks to replace an intermediate link in traditional simulation methods, To achieve improved computing efficiency), as shown in Figure 1.
Figure 1. Data-driven classification of forward electromagnetic calculations
Consequential learning is one of the most straightforward strategies. For example, literature [4] uses CNN instead of the frequency domain finite difference method (FDFD) to solve the Helmholtz equation (see Figure 2a). The equivalent solver designed in the literature [5] based on the attention mechanism performs well (see Figure 2b). On the given test data set, the RCS prediction accuracy exceeds 98%, and is nearly 100 times better than the moment method. Calculate speedup. As a result, learning is intuitive and efficient, but due to the lack of guidance from physical laws, the solution accuracy and generalization ability are often unsatisfactory.
Accelerating the process learning of intermediate links by intelligent means has also attracted attention. For example, literature [6, 7] proposed the "intelligent absorption boundary" scheme, which respectively uses RNN and Long Short Term Memory (Long Short Term Memory, LSTM) to replace ideal matching. The layer absorption boundary condition (Perfectly Matched Layer, PML) can achieve the absorption effect of multi-layer PML under the condition of a single-layer intelligent boundary. The RNN scheme is faster and can achieve about 2 times the calculation speed, but the absorption effect is not as good as the LSTM scheme. .
Although the process learning scheme introduces more physical information and improves the overall generalization ability compared to the result learning, the computational efficiency gain is usually greatly reduced, and it is rare to observe an improvement of more than 1 order of magnitude. How to further reduce the computational complexity of process learning solutions is also an issue that requires in-depth study in the future.
Figure 2. Partial data-driven forward electromagnetic computing research results
1.2****Physics-driven forward electromagnetic calculations
Physics-driven deep neural networks are represented by PINNs (Physics-Informed Neural Network, PINN). This method improves network approximation capabilities while reducing data dependence, and is particularly suitable for solving small sample learning problems. For example, literature [8] introduced the frequency domain electric field equation as a loss function based on the U-Net architecture, and proposed MaxwellNet to solve the free space scattered light field. As shown in Figure 3(b), this result was applied to guide optical lenses. design[9].
Figure 3. Partial physics driver and operator learning forward calculation research results
1.3****Forward electromagnetic calculation based on operator learning
DeepONet、FNO是目前较流行的神经算子模型，FNO在解决流体问题上的成功也带给了电磁计算启发。文献[10]提出用于求解频域自由空间散射问题的改进FNO，相较简单的U-Net等效求解器，不论是计算精度，还是训练以及推理速度都出现了显著提升。文献[11]提出求解频域Maxwell方程组的扩展FNO，相较于FDFD获得了超过100倍的加速比。
1.4**** Calculation of differentiable forward electromagnetic calculations
The FDTD algorithm itself is differentiable and can be directly embedded into differentiable systems with different functions; on the other hand, the forward simulation process can be accelerated with the support of existing deep learning platforms for parallel computing, as shown in Figure 4(a) [12]. For non-differentiable algorithms (such as high-frequency methods). As shown in Figure 4(b), literature [13] proposed a differentiable synthetic aperture radar (SAR) rendering system that can use gradient descent algorithms to infer three-dimensional information from two-dimensional target images.
Figure 4. Schematic representation of some research results of differentiable forward electromagnetic calculations
Table 1. Comparison of characteristics of four intelligent electromagnetic computing methods
**2. ** Reverse intelligent electromagnetic imaging
Electromagnetic inverse scattering imaging has been widely used in non-destructive testing, geological exploration, cancer detection, safety inspection, etc. However, due to the inherent nonlinearity and ill-conditioned nature of the inverse scattering problem, finding a suitable mapping relationship for inverse scattering imaging is a very challenging problem, especially in high-noise environments.
The advantage of reverse intelligent electromagnetic imaging is that it can learn mapping rules from data, thus eliminating the process of complex electromagnetic model reasoning and construction, as well as the iterative process in the optimization algorithm, greatly improving the efficiency of imaging. At the same time, for specific inverse scattering problems, deep learning networks can learn mapping relationships that imply geometric prior information, which can improve imaging accuracy and even achieve super-resolution imaging that breaks through the imaging resolution limit.
2.1 Purely data-driven reverse intelligent electromagnetic imaging
Literature [14] used the U-Net network to further learn and train three imaging mapping relationships. The outputs of these three mappings are target image inputs, which are the original scattered electric field echo measurement data, the preliminary image generated by the BP algorithm, and Induced current data obtained by principal component analysis. In the article, the author calls these three mapping relationships direct inversion mode, back propagation mode and principal component current mode respectively. After testing, both the backpropagation mode and the principal component current mode can generate ideal target images, but the imaging effect of the direct inversion mode is not good, as shown in Figure 5(b). Figure 5. Reverse intelligent electromagnetic imaging based on U-Net structure
2.2 Reverse intelligent electromagnetic imaging driven by electromagnetic physics
Introducing electromagnetic physics mechanisms or equations into the structural design and error function design of the inverse scattering deep learning network, and customizing a dedicated deep learning model for the inverse scattering problem, can make it easier to learn the nonlinear relationship between input and output.
文献[15]将逆散射迭代优化算法的方程结构引入深度学习网络的结构设计中，级联多层复值残差卷积神经网络模块构建出了专用于逆向智能电磁成像的深度神经网络，称之为DeepNIS，如图6(a)所示。通过仿真和实测都证实了DeepNIS在生成图像质量和计算时间方面都显著优于传统的非线性逆散射方法。
Figure 6. End-to-end reverse intelligent electromagnetic imaging based on iterative optimization algorithm
**3、**昇思MindSpore Elec实践
昇思MindSpore Elec基本涵盖了正向智能电磁仿真和逆向智能电磁成像。
Forward intelligent electromagnetic simulation:
a) 数据驱动：终端手机的AI电磁仿真，仿真精度媲美传统科学计算软件，同时性能提升10倍（结果学习）。“金陵.电磁脑” AI电磁仿真基础模型精度媲美传统方法，效率提升10+倍，而且随着目标规模的增大，该提升将会更加显著（过程学习）。
b) Physical drive: When solving the two-dimensional time domain MaxWell equation based on the PINNs method, the solution accuracy and performance are improved through Gaussian distribution function smoothing, multi-channel residual network combined with sin activation function network structure, and adaptive weighted multi-task learning strategy. are significantly better than other frameworks and methods.
c) Calculation of differentiable forward electromagnetic calculations: The process of solving Maxwell's equations using the finite difference time domain (FDTD) method is equivalent to a circular convolutional network (RCNN). By using MindSpore's differentiable operator to rewrite the update process, we can obtain end-to-end differentiable FDTD. The S-parameter simulation accuracy of the three-dimensional patch antenna is consistent with BenchMark.
Reverse intelligent electromagnetic imaging:
a) Purely data-driven: Generate training data for Ground Penetrating Radar (GPR) inversion based on GPRMAX software, and use the AI model to quickly and accurately obtain the target structure by inputting electromagnetic wave signals.
b) Electromagnetic physics driver: Solve the electromagnetic inverse scattering problem of the two-dimensional TM mode based on end-to-end differentiable FDTD. The relative dielectric constant SSIM obtained by the inversion reaches 0.9635, which is highly consistent with the target (right in the figure below); the AI method of Physics-assisted GAN is used to conduct unsupervised learning for the metasurface holographic imaging design, avoiding The production process of the data set, and compared with the traditional GS algorithm, it has better performance in terms of indicators and visual experience.
**4、** Outlook
昇思MindSpore Elec在智能电磁方面已经开展了许多工作，我们也欢迎广大的科学计算爱好者和研究者加入，共同拓展和维护昇思MindSpore Elec套件。
references
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[3] https://gitee.com/mindspore/mindscience/tree/master/MindElec
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