Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior. Machine learning methods that are used to produce the surrogate model should therefore address these problems by providing a scheme to keep the number of queries small, e.g. by using active learning and be able to capture the nonlinear and nonstationary properties of the system. One way of modeling the nonstationarity is to induce input-partitioning, a principle that has proven to be advantageous in active learning for Gaussian processes. However, these methods either assume a known partitioning, need to introduce complex sampling schemes or rely on very simple geometries. In this work, we present a simple, yet powerful kernel family that incorporates a partitioning that: i) is learnable via gradient-based methods, ii) uses a geometry that is more flexible than previous ones, while still being applicable in the low data regime. Thus, it provides a good prior for active learning procedures. We empirically demonstrate excellent performance on various active learning tasks.

翻译：学习复杂计算机模拟和物理机器的精确替代模型通常需要耗时或昂贵的实验。此外，建模的物理依赖关系表现出非线性和非平稳行为。用于生成替代模型的机器学习方法应通过提供方案来解决这些问题，以保持查询次数较少（例如使用主动学习）并能够捕捉系统的非线性和非平稳特性。建模非平稳性的一种方法是引入输入划分，这一原则已被证明在高斯过程的主动学习中具有优势。然而，这些方法要么假设已知划分，要么需要引入复杂的采样方案，要么依赖于非常简单的几何形状。在这项工作中，我们提出了一种简单而强大的核族，其整合了一种划分：i) 可通过基于梯度的方法学习，ii) 使用的几何形状比以往更灵活，同时仍适用于低数据场景。因此，它为主动学习过程提供了良好的先验。我们在各种主动学习任务上实证展示了其卓越性能。