发表机构
Lancaster University, UK; UK Atomic Energy Authority（兰卡斯特大学（英国）; 英国原子能管理局）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对状态保持约束下贝叶斯优化在高度各向异性可行集上的缺陷，提出通过线性化约束响应定义椭球抽取候选解的方法，并在托卡马克偏滤器优化应用中验证了其有效性。
AI 中文摘要
在许多工程设计问题中，目标函数和约束条件依赖于状态：即由设计参数确定的偏微分方程（PDE）的解。我们考虑在将选定的状态可观测量保持在可信值附近的同时改进设计，这一过程我们称之为状态保持约束。带约束的贝叶斯优化通过学习到的可行性模型处理这类问题，但在该问题高度各向异性的可行集上表现不佳。我们的核心思路是预先计算那些线性化约束响应保持在容差范围内的控制量集合，从而将状态空间约束拉回设计空间。该线性化过程定义了一个椭球，我们可以从中高效抽取大量分布均匀的候选解。底层的线性响应映射会在线优化，椭球也会随之重建。我们在核心应用——等离子体边界保持下的托卡马克偏滤器优化上，端到端地验证了该方法的有效性。
英文摘要
In many engineering design problems, the objective and constraints depend on the state: the solution of a PDE determined by the design parameters. We consider improving a design while holding selected state observables near trusted values, which we call state preservation constraints. Constrained Bayesian optimisation handles these with a learnt feasibility model, but struggles with this problem's highly anisotropic feasible set. Our central idea is to pre-compute the set of controls whose linearised constraint response stays within tolerance, thereby pulling back the state-space constraint into design space. This linearisation defines an ellipsoid from which we can efficiently draw a large number of well-spread candidates. The underlying linear response map is refined online, and the ellipsoid is rebuilt accordingly. We demonstrate the method end-to-end on our key application - Tokamak divertor optimisation under plasma-boundary preservation.
