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：从可观测数据中揭示演化系统的控制方程至关重要且富有挑战性。本文考虑一个新场景：从流式数据中发现控制方程。现有方法将测量数据视为整体来发现控制微分方程，因而难以应对该任务。我们提出一种在线建模方法，通过建模流式数据而非处理整个数据集，能够逐个顺序处理样本。该方法在从流式数据中发现常微分方程（ODEs）和偏微分方程（PDEs）时表现良好。演化系统随时间变化，系统状态亦随之改变，因此精确识别变化点至关重要。系统变化后生成的测量数据分布与先前不同，所提方法可识别此差异。在三个混合系统和两个切换线性系统中，我们的方法在识别变化点和发现控制微分方程方面具有竞争力。