Global stochastic optimization of stellarator coil configurations
Global stochastic optimization of stellarator coil configurations
复制标题
仿星器线圈配置的全局随机优化
DOI：
10.1017/s002237782200023x
复制
发表时间：
2021
影响因子：
2.5
通讯作者：
D. Bindel
中科院分区：
文献类型：
--
作者：
Silke Glas;Misha Padidar;Ariel E. Kellison;D. Bindel
在仿星器的构造中，线圈系统的制造和组装是主要成本。这些线圈需要满足严格的工程公差，如果不满足这些公差，该项目可能会被取消，就像国家紧凑型仿星器实验（NCSX）项目（R.L. Orbach，2008，https：//ncsx.pppl.gov/DOE_NCSX_052208. pdf）。因此，我们的目标是找到线圈配置，增加结构公差，而不影响磁场的性能。在本文中，我们开发了一个基于梯度的随机优化模型，寻求强大的仿星器线圈配置在高维。特别是，我们设计了一个两步的方法：第一，我们执行一个近似的全局搜索的样本有效的信任区域贝叶斯优化;第二，我们细化的最小值在第一步中发现的随机局部优化。为此，我们引入两个随机局部优化：BFGS适用于样本平均近似;和亚当，配备了一个控制变量的方差减少。对W7-X型线圈配置进行的数值模拟表明，我们的全局优化方法找到了各种有前途的本地解决方案，在不到0.1美元，\%$的成本以前的工作，这仅仅是考虑局部随机优化。
In the construction of a stellarator, the manufacturing and assembling of the coil system is a dominant cost. These coils need to satisfy strict engineering tolerances, and if those are not met the project could be cancelled as in the case of the National Compact Stellarator Experiment (NCSX) project (R.L. Orbach, 2008, https://ncsx.pppl.gov/DOE_NCSX_052208.pdf). Therefore, our goal is to find coil configurations that increase construction tolerances without compromising the performance of the magnetic field. In this paper, we develop a gradient-based stochastic optimization model which seeks robust stellarator coil configurations in high dimensions. In particular, we design a two-step method: first, we perform an approximate global search by a sample efficient trust-region Bayesian optimization; second, we refine the minima found in step one with a stochastic local optimizer. To this end, we introduce two stochastic local optimizers: BFGS applied to the sample average approximation; and Adam, equipped with a control variate for variance reduction. Numerical simulations performed on a W7-X-like coil configuration demonstrate that our global optimization approach finds a variety of promising local solutions at less than $0.1\,\%$ of the cost of previous work, which considered solely local stochastic optimization.