Taming complexity in computational electromagnetism: a model order reduction approach

电磁现象在集成电路(IC)和天线中发挥着关键作用，这些集成电路和天线为我们周围的许多电子系统提供动力，包括智能手机、计算机和数据中心。在幕后，电磁在物联网(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200亿台物联网设备连接到互联网。由于地面基础设施的高昂成本，电磁波和天线技术的重大进步将是将无数未来的物联网设备连接到互联网的唯一途径。超表面天线是一种新型天线，非常适合响应不断飙升的物联网需求。不幸的是，变形曲面极其复杂。由于没有现有的电磁模拟器能够处理它们的复杂性，工程师们目前缺少最关键的变形表面设计工具之一。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IC，包括先进的人工智能应用越来越需要的神经网络硬件加速器。 电磁求解器的功能与设计者的需求之间的巨大差距是工业界和学术界都面临的一个重大问题。这项拟议的研究旨在通过奠定具有出色可扩展性的电磁解算器的理论和算法基础来填补这一空白。我们建议研究一种基于模型降阶概念的创新方法。虽然模型降阶已被很好地用于电路模拟，但它在计算电磁学中受到的关注有限，尽管有明显的需求。我们建议开发第一个系统的技术来创建紧凑的、降低复杂性的复杂对象的电磁行为模型，例如超表面的单元格。所提出的模型将与基于矩方法的主流模拟器兼容，允许设计者在合理的时间内分析非常大的布局。利用拟议的开发和并行计算，我们将创建一个具有前所未有的可扩展性的电磁求解器，能够处理整个超表面天线。这些发展将极大地促进新的变表面天线和IC的设计，包括即将到来的物联网和人工智能应用所需的天线和IC。 拟议的开发将立即转化为真正的设计工作流程，与领先的公司(AMD，泰利斯)和科学家(教授。Eleftheriade和Hum)。拟议的研究将涉及9名学生，他们将接受最高质量的综合培训，获得世界级的工业合作伙伴、设施和前沿技术。总体而言，该项目预计将培养出9名拥有独特技能的毕业生，受到工业界和学术界的高度需求。

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.