论文标题
来自数据的粗粒和新兴分布式参数系统
Coarse-grained and emergent distributed parameter systems from data
论文作者
论文摘要
我们从时空数据中探讨了分布式参数系统演化定律的推导（尤其是部分微分算子和相关的部分微分方程，PDES）。当然，这是一个经典的识别问题。我们这里的重点是使用流形学习技术（尤其是扩散图的变化）与神经网络学习算法结合使用，这些算法使我们能够在依赖变量甚至PDE的自变量的情况下尝试此任务，甚至不知道PREVIRI，并且必须是从数据中得出的。在扩散图中使用的相似性度量量度用于依赖于粗糙的可变检测，涉及局部粒子分布观测值之间的距离；对于独立变量检测，我们使用局部短时动力学之间的距离。我们通过说明性的PDE示例来演示每种方法。这种无变量的新兴空间识别算法与无方程式多尺度计算工具自然连接。
We explore the derivation of distributed parameter system evolution laws (and in particular, partial differential operators and associated partial differential equations, PDEs) from spatiotemporal data. This is, of course, a classical identification problem; our focus here is on the use of manifold learning techniques (and, in particular, variations of Diffusion Maps) in conjunction with neural network learning algorithms that allow us to attempt this task when the dependent variables, and even the independent variables of the PDE are not known a priori and must be themselves derived from the data. The similarity measure used in Diffusion Maps for dependent coarse variable detection involves distances between local particle distribution observations; for independent variable detection we use distances between local short-time dynamics. We demonstrate each approach through an illustrative established PDE example. Such variable-free, emergent space identification algorithms connect naturally with equation-free multiscale computation tools.
