Physics-informed neural network for solving coupled Korteweg-de Vries equations

Abstract

The studies of coupled partial differential equations are focus of engineering and applied mathematics. Although traditional numerical methods have been widely used, researchers are still looking for new methods to solve coupled partial differential equations. In this paper, physical information neural network (PINN) is introduced to solve one-dimensional coupled Korteweg-de Vries (cKdV) equations. Compared with the traditional neural network, the innovation of PINN is to embed the physical constraints of the equations into the network loss function. Moreover, within the acceptable relative error range, the solution can take a longer single time step than the presently available. The results revealed that PINN can solve the cKdV equations with reasonable errors only by training a small amount of data.