Data-driven and physical-based identification of partial differential equations for multivariable system

Data-driven partial differential equation identification is a potential breakthrough to solve the lack of physical equations in complex dynamic systems. However, existing equation identification methods still cannot effectively identify equations from multivariable complex systems. In this work, we combine physical constraints such as dimension and direction of equation with data-driven method, and successfully identify the Navier-Stocks equations from the flow field data of Karman vortex street. This method provides an effective approach to identify partial differential equations of multivariable complex systems.