Physics informed neural network for forward and inverse multispecies contaminant transport with variable parameters

Abstract

Multispecies contaminant transport occurs frequently in groundwater systems. Currently, most solutions to multispecies transport problems do not consider parameter variability which has a determinant impact on concentration distribution. In this paper, a physics-informed neural network (PINN) containing a locally adaptive residual network and a probabilistic point selection strategy referred to as RP-PINN is proposed to solve the forward and inverse problems of multispecies contaminant transport with variable parameters. The RP-PINN model solves the contaminant transport problem by embedding a system of partial differential equations (PDEs) into the loss function of the deep neural network. The effect of spatiotemporally varying dispersion coefficient and transport velocity on contaminant transport was analyzed. Three transport systems with four different temporal functions were investigated. Results showed that although the original PINN yielded reasonable solutions to multispecies contaminant transport problems with variable parameters, the RP-PINN had better fitting ability and stability. For the inverse problem of model coefficient identification, RP-PINN accurately learnt the diffusion coefficients and transport velocities varying in space and time, which dynamically helped correct the model parameters.