Taming complexity in computational electromagnetism: a model order reduction approach

电磁现象在集成电路（ic）和天线中起着至关重要的作用，这些电路和天线为我们周围的许多电子系统提供了支持，包括智能手机、计算机和数据中心。在幕后，电磁学在物联网（IoT）和人工智能（AI）等新兴技术中也发挥着至关重要的作用。据估计，到2020年，将有200亿个物联网设备连接到互联网。由于地面基础设施的成本过高，电磁波和天线技术的重大进步将是将无数未来物联网设备连接到互联网的唯一途径。超表面是一种新型天线，非常适合应对飙升的物联网需求。不幸的是，超表面非常复杂。由于没有现有的电磁模拟器可以处理它们的复杂性，工程师们目前缺少一种最关键的超表面设计工具。AMD等微电子公司也面临着类似的挑战，它们广泛依赖电磁模拟器来设计新的集成电路，包括高级人工智能应用日益需要的神经网络硬件加速器。

Electromagnetic phenomena play a critical role inside the integrated circuits (ICs) and antennas that empower many electronic systems around us, including smartphones, computers, and data centers. Behind the scenes, electromagnetism also plays a crucial role in emerging technologies such as the Internet of Things (IoT) and Artificial Intelligence (AI). It is estimated that, by 2020, 20 billion IoT devices will be connected to the Internet. Electromagnetic waves, and significant advancements in antenna technology, will be the only way to connect the myriad of future IoT devices to the Internet, due to the prohibitive cost of terrestrial infrastructure. Metasurfaces are a new type of antennas which is ideally suited to respond to soaring IoT needs. Unfortunately, metasurfaces are extremely complex. Since no existing electromagnetic simulator can handle their complexity, engineers are currently missing one of the most critical tools for metasurface design. Similar challenges are faced by microelectronic companies such as AMD, which extensively rely on electromagnetic simulators to design new ICs, including the hardware accelerators of neural networks that are increasingly needed by advanced AI applications. The significant gap between what electromagnetic solvers can do and what designers need is a major issue for both industry and academia. The proposed research aims to fill this gap by laying down the theoretical and algorithmic foundations of an electromagnetic solver with superior scalability. We propose to investigate an innovative approach based on the concept of model order reduction. While model order reduction is well established for circuit simulation, it has received limited attention in computational electromagnetism, despite a clear need. We propose to develop the first systematic techniques to create compact, reduced-complexity models of the electromagnetic behavior of complex objects, such as the unit cell of a metasurface. The proposed models will be compatible with mainstream simulators based on the method of moments, allowing designers to analyze very large layouts in reasonable time. Leveraging the proposed developments and parallel computing, we will create an electromagnetic solver with unprecedented scalability, capable of handling an entire metasurface antenna. These developments will greatly facilitate the design of new metasurface antennas and ICs, including those required by upcoming IoT and AI applications. The proposed developments will be immediately translated to real design workflows, in collaboration with leading companies (AMD, Thales) and scientists (Profs. Eleftheriades and Hum). The proposed research will involve nine students who will receive comprehensive training of the highest quality, with access to world-class industrial partners, facilities and forefront technologies. Overall, this program is expected to result in nine graduates with a unique skillset, in high demand by industry and academia.