由时间序列深度重构奇异吸引子
Deep reconstruction of strange attractors from time series
摘要：
物理系统的实验测量通常只有有限数量的独立通道，导致基本的动力学变量无法被观测到。然而，许多流行的方法无监督推理的潜在动力学实验数据隐含假设的测量具有更高的内在维数比底层系统-使坐标识别降维问题。在这里，我们研究相反的限制，其中隐藏的管理坐标必须推断出只有一个低维的时间序列的测量。受经典的混沌吸引子的部分观测分析技术的启发，我们引入了一个通用的嵌入技术的单变量和多变量的时间序列，由一个新的潜在空间损失函数训练的自编码器。我们表明，我们的技术比现有技术更好地重建了合成和现实世界系统的奇怪吸引子，并且它甚至可以创建一致的，预测性的表示随机系统。最后，我们使用我们的技术来发现动态吸引子在不同的系统，如病人的心电图，家庭用电，神经尖峰，和老忠实间歇泉的爆发-展示了我们的技术探索性数据分析的不同应用。
英文摘要：
Experimental measurements of physical systems often have a limited number of independent channels, causing essential dynamical variables to remain unobserved. However, many popular methods for unsupervised inference of latent dynamics from experimental data implicitly assume that the measurements have higher intrinsic dimensionality than the underlying system---making coordinate identification a dimensionality reduction problem. Here, we study the opposite limit, in which hidden governing coordinates must be inferred from only a low-dimensional time series of measurements. Inspired by classical analysis techniques for partial observations of chaotic attractors, we introduce a general embedding technique for univariate and multivariate time series, consisting of an autoencoder trained with a novel latent-space loss function. We show that our technique reconstructs the strange attractors of synthetic and real-world systems better than existing techniques, and that it creates consistent, predictive representations of even stochastic systems. We conclude by using our technique to discover dynamical attractors in diverse systems such as patient electrocardiograms, household electricity usage, neural spiking, and eruptions of the Old Faithful geyser---demonstrating diverse applications of our technique for exploratory data analysis.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
