Rapid and Robust High Order Spectral Solvers for Learning Photonic Structures

用于学习光子结构的快速、鲁棒的高阶谱求解器

• 批准号: 2111283
• 负责人: David Nicholls
• 金额: $ 42.08万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2111283&HistoricalAwards=false
• 关键词: Rapid; Robust; Order; Spectral; Solvers

Over the past two decades engineers have built optical devices with stunning capabilities of detection, sensing, and imaging. While intuition has been an invaluable guide in pushing the envelope of what is possible, the increasing complexity of design and the wide array of available components is rendering this approach ever more difficult. For this reason, numerical simulation has become an invaluable tool. As this approach becomes ever more pervasive, the search for rapid, robust, and highly accurate algorithms has become quite acute. The PI will enhance his class of simulation tools by exploring new avenues of numerical approximation, novel paths to enforcing the governing equations, and appealing to the powerful methods of Machine Learning (in particular, Deep Learning) to discover optimal parameter values for device design. The PI will also develop a rigorous analysis of these new numerical schemes in order to evaluate and validate their real-world performance. This project will provide support for one graduate student each year of the three year award.Over the past two decades engineers have built optical devices with stunning capabilities of detection, sensing, and imaging. While intuition and linearized models have been invaluable guides in pushing the envelope of what is possible, the increasing complexity of design and the wide array of available components is rendering this approach ever more difficult. For this reason, numerical simulation has become an invaluable tool. As this approach becomes ever more pervasive, the search for rapid, robust, and highly accurate algorithms has become quite acute. The PI will enhance his class of High-Order Spectral solvers with the following objectives: (1) Incorporating two-dimensional materials into his rapid and highly accurate three-dimensional "Field Expansions" vector Maxwell equation solver; (2) Expand his "High-Order Perturbation of Surfaces/Asymptotic Waveform Evaluation" algorithm for joint geometry/frequency perturbation to the three-dimensional vector Maxwell equations; (3) Extend his "High-Order Perturbation of Envelopes" algorithm for structural perturbations to this three--dimensional case; (4) Provide rigorous analytical justification for each of the latter two; and (5) Bring to bear the powerful new tools of Deep Learning to discover optimal parameter values for device design.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

在过去的二十年中，工程师建造了具有惊人检测，传感和成像功能的光学设备。 虽然直觉一直是推动可能的信封的宝贵指南，但设计的复杂性日益增加和广泛的可用组件却使这种方法变得更加困难。因此，数值模拟已成为宝贵的工具。随着这种方法变得越来越普遍，寻找快速，健壮且高度准确的算法变得非常敏锐。 PI将通过探索数值近似的新途径，执行管理方程式的新途径，并吸引强大的机器学习方法（尤其是深度学习）来发现设备设计的最佳参数值，从而增强他的模拟工具。 PI还将对这些新的数值方案进行严格的分析，以评估和验证其现实世界的性能。该项目将为每年三年奖项的一名研究生提供支持。在过去的二十年中，工程师已经建造了具有惊人检测，感应和成像功能的光学设备。 虽然直觉和线性化模型在推动可能的信封方面是无价的指南，但设计的复杂性日益增强，可用组件的广泛阵列使这种方法变得更加困难。 因此，数值模拟已成为宝贵的工具。 随着这种方法变得越来越普遍，寻找快速，健壮且高度准确的算法变得非常敏锐。 PI将通过以下目标增强他的高阶光谱求解器类别：（1）将二维材料纳入他的快速且高度准确的三维“场膨胀”矢量Maxwell方程求解器； （2）扩展了他的“表面/渐近波形评估的高阶扰动”算法，用于连接几何/频率扰动到三维矢量麦克斯韦方程； （3）扩展了他的“信封的高阶扰动”算法，以实现这种三维情况的结构扰动； （4）为后两点提供严格的分析辩护； （5）带来深入学习的强大新工具，以发现设备设计的最佳参数值。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响评估标准通过评估来支持的。

项目成果

A high–order spectral algorithm for the numerical simulation of layered media with uniaxial hyperbolic materials

用于单轴双曲材料层状介质数值模拟的高阶谱算法

• DOI: 10.1016/j.jcp.2022.110961
• 发表时间: 2022
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Nicholls, David P.

Data-Driven Design of Thin-Film Optical Systems using Deep Active Learning

使用深度主动学习的薄膜光学系统的数据驱动设计

• DOI: 10.1364/oe.459295
• 发表时间: 2022
• 期刊: Optics express
• 影响因子: 3.8
• 作者: Hong, Y.;Nicholls, D.
• 通讯作者: Nicholls, D.

Joint Geometry/Frequency Analyticity of Fields Scattered by Periodic Layered Media

• DOI: 10.1137/22m1477568
• 发表时间: 2023-06
• 期刊: SIAM Journal on Mathematical Analysis
• 影响因子: 2
• 作者: Matthew Kehoe;D. Nicholls