Koopman neural operator as a mesh-free solver of non-linear partial differential equations

Wei Xiong, Xiaomeng Huang, Ziyang Zhang, Ruixuan Deng, Pei Sun, Yang Tian

Abstract: Highlights•We propose a new neural operator model for partial differential equation (PDE) solving and realize an effective linear prediction of non-linear dynamics via Koopman operator.•Our approach achieves robust and accurate modeling of the long-term non-linear dynamics of PDE families or real systems.•Our model may serve as a basic unit for constructing new frameworks of PDE solving and dynamic system modeling.