发表机构
Systems Research Institute, Polish Academy of Sciences; Space Research Centre, Polish Academy of Sciences（波兰科学院系统研究所; 波兰科学院空间研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究在不知潜在动力学时最优放置有限传感器重建高维信号的问题，将其转化为弱凸约束投影问题，用不精确切割球算法计算ε全局解，还提出逆切割球算法，并用NACA翼型压力重建评估框架。
AI 中文摘要
我们研究在不了解潜在动力学的情况下，如何最优地放置有限数量的传感器来重建高维信号。该任务被表述为非凸组合优化问题，并重新表述为弱凸约束投影问题。这种重新表述使我们能够使用不精确切割球算法计算ε全局解。我们还提出了逆切割球算法，它从任何可行的启发式解开始，要么将其改进到规定的容差ε，要么证明其ε全局最优性。我们使用XFOIL数据在NACA翼型的压力重建上评估了该框架。
英文摘要
We address the problem of optimally placing a limited number of sensors to reconstruct high-dimensional signals without knowledge of the underlying dynamics. The task is formulated as a nonconvex combinatorial optimisation problem and recast as a weakly convex constrained projection problem. This reformulation allows us to compute $\varepsilon$-global solutions using the Inexact Cutting Sphere algorithm. We further propose the Inverse Cutting Sphere algorithm, which starts from any feasible heuristic solution and either improves it by a prescribed tolerance $\varepsilon$ or certifies its $\varepsilon$-global optimality. The framework is evaluated on pressure reconstruction for NACA airfoils using XFOIL data.
