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

• Published in: Journal of hydrology (Amsterdam) Vol. 655; p. 132977
• Main Authors: Hou, Qingzhi, Xu, Xiaolong, Sun, Zewei, Wang, Jianping, Singh, Vijay P.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2025
• Subjects: Convection–diffusion-reaction systems; dispersibility; groundwater; Inverse problem; Multispecies transport; Physics-informed neural network; space and time; Variable parameter; Variable parameter; Physics-informed neural network; Multispecies transport; Convection–diffusion-reaction systems; Inverse problem
• ISSN: 0022-1694
• DOI: 10.1016/j.jhydrol.2025.132977

•Multicomponent system with variable coefficients is studied by PINN for the first time.•Locally adaptive residual network is used to solve the nonlinear transport system.•Probabilistic point selection strategy is introduced for collocation points resampling.•The error of RP-PINN is one order of magnitude lower than that of the original PINN.•Variable coefficients are accurately identified by RP-PINN with limited data. 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.