从多领域时间序列中学习可解释的分层动力系统模型
Learning Interpretable Hierarchical Dynamical Systems Models from Time Series Data
- 构建分层框架，融合多领域数据保留单域特征
- 发现低维特征空间，其与系统控制参数呈线性关系
- 支持跨参数域迁移学习，适合动态系统建模研究者
在科学领域，我们常需从观测的时间序列中构建底层系统动态的生成模型。尽管单一领域数据的动力系统重构（DSR）方法已很强大，但如何有效整合多动态模式的数据并用于泛化仍是开放问题，尤其当单条时间序列较短时，群体信息可弥补个体数据不足。本文提出一种分层框架，既能利用多领域群体信息，又能保持各单域特性，并在主流DSR基准及神经科学、医学数据上验证。该方法不仅能准确重建所有独立动态模式，还通过无监督学习发现共有的低维特征空间，使具有相似动态的数据集自然聚类。这些特征空间中的变量与系统控制参数存在显著线性关系，具有高度可解释性。最后，展示了对新参数区间的迁移学习与泛化能力，为构建动力系统基础模型铺平道路。
原文摘要 · Abstract (English)
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. Here we introduce a hierarchical framework that enables to harvest group-level (multi-domain) information while retaining all single-domain characteristics, and showcase it on popular DSR benchmarks, as well as on neuroscience and medical data. 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, paving the way toward DSR foundation models.
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