Alexander Luce, Rasoul Alaee, Fabian Knorr and Florian Marquardt
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引用次数: 0
摘要
优化物理设备的形状和拓扑结构对科学和技术进步至关重要,因为这对众多行业和研究领域都有广泛影响。形状和拓扑优化方面的创新已经遍及各个领域,特别是结构力学、流体力学和最近的光子学。基于梯度的逆向设计技术在解决光子和光学问题方面尤为成功,其集成化、微型化硬件为设备性能设定了新标准。要计算梯度,通常有两种方法:一是使用自动微分(AD)实现专门的求解器,二是手工推导梯度计算和邻接源的解析解。在这项工作中,我们提出了一个中间方案,并提出了一种混合方法,即利用自动微分的优势处理梯度推导,同时使用现有的、经过验证的黑盒光子求解器进行数值求解。利用邻接法,我们使现有的数值求解器可微分,并将其无缝集成到 AD 框架中。此外,这还能让用户将优化环境与机器学习、几何生成或复杂的后处理等其他自动可微分组件无缝集成,从而实现更好的光子设计工作流程。我们通过两个不同的光子优化问题来说明这种方法:优化光学纳米腔附近磁偶极子的珀塞尔因子和提高 µLED 的光提取效率。
Merging automatic differentiation and the adjoint method for photonic inverse design
Optimizing the shapes and topology of physical devices is crucial for both scientific and technological advancements, given their wide-ranging implications across numerous industries and research areas. Innovations in shape and topology optimization have been observed across a wide range of fields, notably structural mechanics, fluid mechanics, and more recently, photonics. Gradient-based inverse design techniques have been particularly successful for photonic and optical problems, resulting in integrated, miniaturized hardware that has set new standards in device performance. To calculate the gradients, there are typically two approaches: namely, either by implementing specialized solvers using automatic differentiation (AD) or by deriving analytical solutions for gradient calculation and adjoint sources by hand. In this work, we propose a middle ground and present a hybrid approach that leverages and enables the benefits of AD for handling gradient derivation while using existing, proven but black-box photonic solvers for numerical solutions. Utilizing the adjoint method, we make existing numerical solvers differentiable and seamlessly integrate them into an AD framework. Further, this enables users to integrate the optimization environment seamlessly with other autodifferentiable components such as machine learning, geometry generation, or intricate post-processing which could lead to better photonic design workflows. We illustrate the approach through two distinct photonic optimization problems: optimizing the Purcell factor of a magnetic dipole in the vicinity of an optical nanocavity and enhancing the light extraction efficiency of a µLED.
期刊介绍:
Machine Learning Science and Technology is a multidisciplinary open access journal that bridges the application of machine learning across the sciences with advances in machine learning methods and theory as motivated by physical insights. Specifically, articles must fall into one of the following categories: advance the state of machine learning-driven applications in the sciences or make conceptual, methodological or theoretical advances in machine learning with applications to, inspiration from, or motivated by scientific problems.