稀疏多项式混沌算法与差异适应设计域用于不确定性量化和格子结构的优化
Applied optics
|August 12, 2025
概括
本研究介绍了一种多项式混沌扩展 (PCE) 算法,用于在格子过器中高效量化不确定性. 与传统技术相比,该方法显著降低了计算成本,使得优化速度更快.
科学领域:
- 计算电磁学的计算.
- 光学和光学工程的光学和光学工程.
- 不确定性量化不确定性的量化.
背景情况:
- 网格过器是关键的光学元件,但它们的性能分析涉及复杂的模拟.
- 不确定性量化 (UQ) 对于可靠的过器设计至关重要,但计算密集.
- 像蒙特卡洛 (MC) 这样的现有方法需要广泛的模拟,限制设计优化.
研究的目的:
- 为网格过器的UQ开发一个计算效率高的算法.
- 为了使网格过器性能更快,更可靠地进行优化.
- 为了减少对耗时的全波溶解器的依赖.
主要方法:
- 使用多项式混沌扩展 (PCEs) 进行自适应的无otropic 模型构建.
- 使用最小角度回归 (LARS) 稀疏解决方案来计算PCE系数.
- 基于局部样本变异来设计最佳实验,以提高可靠性.
- 将PCE与Kriging插值集成在一起,以改善优化.
主要成果:
- 基于PCE的方法与全波溶解器相比,实现了超过2个数量级的加速度.
- 需要大约25个全波解决器调用,而MC需要2万个.
- PCE模型有效地生成样本以进行优化,性能优于直接的全波溶解器采样.
- 结合PCE和Kriging可以获得更好的优化结果.
结论:
- 拟议的PCE算法为格过器中的UQ提供了高效和可靠的解决方案.
- 这种方法显著加快了光子设备的设计和优化周期.
- 该方法提供了一个强大的框架,用于将UQ与光学工程中的优化集成在一起.
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