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.

中文翻译：

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非线性时间序列的深度学习：推断慢驱动力的示例

观测动态的记录通常以时间序列的形式进行。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建设性映射。在成功的应用程序中，此类输入通常准备为静态图像。因此，在这里我们提出了两种方法来准备这些输入，以学习时间序列背后的动态特性。在第一种方法中，我们简单地将一个矩形形状的时间序列排列为图像。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。