标题： 用于时空模拟器的高阶奇异值分解张量模拟器 显示英文标题

标题： A higher-order singular value decomposition tensor emulator for spatio-temporal simulators

摘要： 我们介绍了一种方法，用于构建环境和生态时空过程的模拟器，该方法使用高阶奇异值分解（HOSVD）作为奇异值分解（SVD）方法的扩展。 该方法的一些重要优点是，它允许使用监督学习方法（例如随机森林和高斯过程回归）的组合，并且允许预测在训练样本中未使用的空间位置和时间点的过程值。 该方法通过两个应用进行演示：第一个是冰川学中浅冰近似偏微分方程的周期解，第二个是集体动物运动的基于代理的模型。 在两种情况下，我们都展示了结合不同机器学习模型进行准确模拟的价值。 此外，在基于代理的模型情况下，我们展示了张量模拟器成功捕捉空间和时间个体行为的能力。 我们通过一个真实数据示例展示了执行贝叶斯推断以学习支配集体动物行为参数的能力。 显示英文摘要

摘要： We introduce methodology to construct an emulator for environmental and ecological spatio-temporal processes that uses the higher order singular value decomposition (HOSVD) as an extension of singular value decomposition (SVD) approaches to emulation. Some important advantages of the method are that it allows for the use of a combination of supervised learning methods (e.g., random forests and Gaussian process regression) and also allows for the prediction of process values at spatial locations and time points that were not used in the training sample. The method is demonstrated with two applications: the first is a periodic solution to a shallow ice approximation partial differential equation from glaciology, and second is an agent-based model of collective animal movement. In both cases, we demonstrate the value of combining different machine learning models for accurate emulation. In addition, in the agent-based model case we demonstrate the ability of the tensor emulator to successfully capture individual behavior in space and time. We demonstrate via a real data example the ability to perform Bayesian inference in order to learn parameters governing collective animal behavior.