用梯度信息提升光子器件逆向设计效率，避免局部最优。
Gradient-Informed Bayesian and Interior Point Optimization for Efficient Inverse Design in Nanophotonics
- 结合神经网络代理模型与内点优化，利用梯度指导采样点选择。
- 10层布拉格反射镜均方误差仅4.5%，优于文献中16层的7.8%。
- 适合需要高精度、快速优化的纳米光子器件设计者。
逆向设计，尤其是几何形状优化，为开发高性能纳米光子器件提供了系统性方法。尽管已有多种优化算法，但以往全局方法收敛慢，而局部搜索策略常陷入局部最优。为此，我们提出BONNI：基于神经网络集成代理模型的贝叶斯优化与内点优化相结合的方法。该方法通过引入梯度信息高效确定采样点，克服了纳米光子应用中常见的局部最优问题，同时发挥梯度优化的效率优势。我们在分布式布拉格反射镜和双层光栅耦合器的设计中，对多种常用优化算法进行了全面对比。使用BONNI，仅用4.5%的均方谱误差实现了10层分布式布拉格反射镜设计，优于此前文献报道的16层7.8%误差结果。此外，宽带波导锥形器和光子晶体波导过渡结构的设计进一步验证了BONNI的有效性。
原文摘要 · Abstract (English)
Inverse design, particularly geometric shape optimization, provides a systematic approach for developing high-performance nanophotonic devices. While numerous optimization algorithms exist, previous global approaches exhibit slow convergence and conversely local search strategies frequently become trapped in local optima. To address the limitations inherent to both local and global approaches, we introduce BONNI: Bayesian optimization through neural network ensemble surrogates with interior point optimization. It augments global optimization with an efficient incorporation of gradient information to determine optimal sampling points. This capability allows BONNI to circumvent the local optima found in many nanophotonic applications, while capitalizing on the efficiency of gradient-based optimization. We demonstrate BONNI's capabilities in the design of a distributed Bragg reflector as well as a dual-layer grating coupler through an exhaustive comparison against other optimization algorithms commonly used in literature. Using BONNI, we were able to design a 10-layer distributed Bragg reflector with only 4.5% mean spectral error, compared to the previously reported results of 7.8% error with 16 layers. Further designs of a broadband waveguide taper and photonic crystal waveguide transition validate the capabilities of BONNI.
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