Discovering the governing equations of evolving systems from available observations is essential and challenging. However, current methods does not capture the situation that underlying system dynamics can be changed.Evolving systems are changing over time, which invariably changes with system status. Thus, finding the exact change points is critical. 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, partial differential equations (PDEs), and high-dimensional PDEs from streaming data. The measurement generated from a changed system is distributed dissimilarly to before; hence, the difference can be identified by the proposed method. Our proposal performs well in identifying the change points and discovering governing differential equations in two evolving systems.
翻译：从现有观测中发现不断发展的系统的管理方程式既重要又富有挑战性。然而,目前的方法并不能反映系统动态可以改变的情况。 演变中的系统随着时间的变化而变化,随着系统状态的变化而变化。 因此,找到精确的变化点至关重要。 我们建议了一种在线模型方法,能够通过对流数据进行建模,而不是处理整个数据集,逐个处理样本。 拟议的方法在发现普通差异方程式、部分差异方程式和流数据的高维PDE方面表现良好。 改变后的系统产生的测量方法与以前不同,因此差异可以通过拟议方法确定。 我们的建议在确定变化点和在两个不断发展的系统中发现差异方程式方面表现良好。
相关内容
微信扫码咨询专知VIP会员