The ability to non‐uniformly weight the input space is desirable for many applications, and has been explored for space‐filling approaches. Increased interests in linking models, such as in a digital twinning framework, increases the need for sampling emulators where they are most likely to be evaluated. In particular, we apply non‐uniform sampling methods for the construction of aerodynamic databases. This paper combines non‐uniform weighting with active learning for Gaussian Processes (GPs) to develop a closed‐form solution to a non‐uniform active learning criterion. We accomplish this by utilizing a kernel density estimator as the weight function. We demonstrate the need and efficacy of this approach with an atmospheric entry example that accounts for both model uncertainty as well as the practical state space of the vehicle, as determined by forward modeling within the active learning loop.

中文翻译：

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高斯过程模型的非均匀主动学习及其在轨迹通知空气动力学数据库中的应用

对输入空间进行非均匀加权的能力对于许多应用来说都是可取的，并且已经在空间填充方法中进行了探索。人们对链接模型（例如在数字孪生框架中）的兴趣增加，增加了对最有可能评估模型的采样模拟器的需求。特别是，我们应用非均匀采样方法来构建空气动力学数据库。本文将非均匀加权与高斯过程（GP）的主动学习相结合，开发非均匀主动学习标准的封闭式解决方案。我们通过利用核密度估计器作为权重函数来实现这一点。我们通过大气进入示例证明了这种方法的必要性和有效性，该示例考虑了模型不确定性以及车辆的实际状态空间，这是由主动学习循环中的正向建模确定的。