We introduce methodology to construct an emulator for environmental and ecological Spatiotemporal 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.

我们介绍了构建环境和生态时空过程仿真器的方法，该仿真器使用高阶奇异值分解 (HOSVD) 作为奇异值分解 (SVD) 仿真方法的扩展。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，并且还允许预测在空间位置和时间点未使用的过程值。训练样本。该方法有两个应用：第一个是冰川学中浅冰近似偏微分方程的周期解，第二个是基于代理的集体动物运动模型。在这两种情况下，我们展示了结合不同机器学习模型进行准确仿真的价值。此外，在基于代理的模型案例中，我们展示了张量模拟器在空间和时间上成功捕获个体行为的能力。我们通过一个真实的数据示例展示了执行贝叶斯推理以学习控制集体动物行为的参数的能力。