Discover governing differential equations from evolving systems

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.