Discovering the governing equations of evolving systems from available observations is essential and challenging. In this paper, we consider a new scenario: discovering governing equations from streaming data. Current methods struggle to discover governing differential equations with considering measurements as a whole, leading to failure to handle this task. We propose an online modeling method capable of handling samples one by one sequentially by modeling streaming data instead of processing the entire dataset. The proposed method performs well in discovering ordinary differential equations (ODEs) and partial differential equations (PDEs) from streaming data. Evolving systems are changing over time, which invariably changes with system status. Thus, finding the exact change points is critical. The measurement generated from a changed system is distributed dissimilarly to before; hence, the difference can be identified by the proposed method. Our proposal is competitive in identifying the change points and discovering governing differential equations in three hybrid systems and two switching linear systems.

翻译：从可用观测中揭示演化系统的控制方程至关重要且极具挑战。本文考虑一种新场景：从流数据中发现控制方程。现有方法将全部测量数据视为整体进行控制微分方程发现，难以应对此类任务。我们提出一种在线建模方法，通过逐序处理流数据样本来替代全数据集处理。该方法能有效从流数据中发现常微分方程（ODEs）与偏微分方程（PDEs）。演化系统随时间变化，系统状态必然发生动态改变，因此精确识别变化点至关重要。系统变化后的测量数据与先前分布不同，所提方法可识别该差异。在三个混合系统与两个切换线性系统中，该方法在识别变化点与发现控制微分方程方面均具有竞争力。