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 techniques for studying the strange attractors of chaotic systems, we introduce a general embedding technique for 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, and eruptions of the Old Faithful geyser---demonstrating diverse applications of our technique for exploratory data analysis.
翻译:物理系统的实验测量往往有数量有限的独立渠道,导致基本动态变量得不到观察。然而,许多从实验数据中不经监督地推断潜在动态的流行方法隐含地假设,这些测量的内在维度高于基本的系统制造协调确定减少维度的问题。这里,我们研究相反的界限,其中隐藏的坐标只能从一个低维时间序列的测量中推断出来。在研究混乱系统奇怪的吸引器的经典技术的启发下,我们为时间序列引入了一种一般嵌入技术,其中包括一个受过新颖潜空空间损失功能训练的自动编码器。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奇怪的吸引器,并创造了甚至是随机系统的一致、预测性表现。我们最后通过利用我们的技术在诸如病人心电图、家庭电用以及老信服的银器的爆发等不同系统中发现动态吸引器,用以进行探索性数据分析。