Deep Learning for Nonlinear Time Series: Examples for Inferring Slow Driving Forces
Deep Learning for Nonlinear Time Series: Examples for Inferring Slow Driving Forces
复制标题
DOI：
10.1142/s0218127420502260
复制
发表时间：
2020-12
期刊：
影响因子：
--
通讯作者：
Yoshito Hirata;K. Aihara
中科院分区：
文献类型：
--
作者：
Yoshito Hirata;K. Aihara
观测动态的记录通常是以时间序列的形式编制的。然而，时间序列可能是深度神经网络学习的一种具有挑战性的数据集类型。在深度神经网络中，输入和输出对通常用于构造性映射。在成功的应用中，这样的输入通常被准备为静态图像。因此，在这里，我们提出了两种方法来准备这样的输入，以学习时间序列背后的动力学特性。在第一种方法中，我们简单地将一个时间序列排列成矩形作为图像。在第二种方法中，我们使用延迟坐标或无阈值递归图将时间序列转换为距离矩阵。我们证明了第二种方法在推断一个缓慢的驱动力从强迫系统的观察，其中有对称性和几乎不变的子集。
Records for observing dynamics are usually complied by a form of time series. However, time series can be a challenging type of dataset for deep neural networks to learn. In deep neural networks, pairs of inputs and outputs are usually fed for constructive mapping. Such inputs are typically prepared as static images in successful applications. And so, here we propose two methods to prepare such inputs for learning the dynamical properties behind time series. In the first method, we simply array a time series in the shape of a rectangle as an image. In the second method, we convert a time series into a distance matrix using delay coordinates, or an unthresholded recurrence plot. We demonstrate that the second method performs well in inferring a slow driving force from observations of a forced system within which there are symmetry and almost invariant subsets.