标题： 电磁学中用于超材料设计的快速近似求解器 显示英文标题

标题： Fast approximate solvers for metamaterials design in electromagnetism

摘要： 在电磁学中，麦克斯韦方程组的模型能够产生准确且可信的预测。 数值求解器可以得到远超解析闭式解集的电磁解；这对于超材料设计至关重要，因为目标是找到生成所需属性最优电磁解的几何结构。 那么，为什么我们仍然需要在超材料研究中创建计算方法？ 为什么我们应该关注解析模型？ 仿真和优化的瓶颈限制了最先进方法的应用范围。 因此，存在创造新计算方法的机会。 针对特定应用类别的半解析方法可以实现仿真和优化。 我们详细介绍了使用光学超表面作为示例的定制方法的研究现状，并提出了最佳实践。 我们还讨论了机器学习如何增强这些方法。 显示英文摘要

摘要： In electromagnetism, the model of Maxwell's equations yields accurate and trustworthy predictions. Numerical solvers can reach electromagnetic solutions far beyond the set of analytical closed-form solutions; this is crucial in metamaterials design where the goal is to find the geometry that generates an optimal electromagnetic solution for a desired property. Then why do we still need to create computational methodologies in metamaterials research? And why should we care about analytical models? The simulation and optimization bottlenecks limit the range of applications of the state of the art. Hence, there is room for opportunities to create new computational methodologies. Semi-analytical methods that are customized for classes of applications enable simulation and optimization. We detail the state of the research in customized methodologies using the illustrative example of optical metasurfaces and suggest best practices. We also discuss how machine learning may enhance these methodologies.