论文标题
时空模拟器的高阶奇异值分解张量模拟器
A higher-order singular value decomposition tensor emulator for spatio-temporal simulators
论文作者
论文摘要
我们介绍了为环境和生态时空过程构建模拟器的方法，该过程使用高阶奇异值分解（HOSVD）作为仿真奇异值分解（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的组合（例如随机森林和高斯过程回归），并且还允许在训练样本中未使用的空间位置和时间点上预测过程值。该方法用两种应用证明：第一个是冰川学浅层近似偏微分方程的周期性解决方案，其次是基于代理的集体动物运动模型。在这两种情况下，我们都证明了将不同的机器学习模型相结合以进行准确仿真的价值。此外，在基于代理的模型案例中，我们证明了张量模拟器成功捕获时空行为的能力。我们通过真实数据示例证明执行贝叶斯推理的能力，以学习有关集体动物行为的参数。
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.
