In science, we are often interested in obtaining a generative model of the underlying system dynamics from observed time series. While powerful methods for dynamical systems reconstruction (DSR) exist when data come from a single domain, how to best integrate data from multiple dynamical regimes and leverage it for generalization is still an open question. This becomes particularly important when individual time series are short, and group-level information may help to fill in for gaps in single-domain data. At the same time, averaging is not an option in DSR, as it will wipe out crucial dynamical properties (e.g., limit cycles in one domain vs. chaos in another). Hence, a framework is needed that enables to efficiently harvest group-level (multi-domain) information while retaining all single-domain dynamical characteristics. Here we provide such a hierarchical approach and showcase it on popular DSR benchmarks, as well as on neuroscientific and medical time series. In addition to faithful reconstruction of all individual dynamical regimes, our unsupervised methodology discovers common low-dimensional feature spaces in which datasets with similar dynamics cluster. The features spanning these spaces were further dynamically highly interpretable, surprisingly in often linear relation to control parameters that govern the dynamics of the underlying system. Finally, we illustrate transfer learning and generalization to new parameter regimes.

本研究解决了如何有效整合来自多个动态领域的数据，以生成系统动态模型的核心问题。提出了一种层次化的方法，能够在保留单一领域动态特性的同时，利用群体级别的信息，促进了对短时间序列的有效重建。研究显示，这种方法能够发现相似动态数据集的共同低维特征空间，并对控制参数与动态之间的关系进行高效解释，具有重要的应用潜力。

从时间序列数据学习可解释的层次动态系统模型