Orthogonal grid physics-informed neural networks: A neural network-based simulation tool for advection–diffusion–reaction problems

Abstract

Stable and accurate reconstruction of pollutant transport is a crucial and challenging problem, including the inverse problem of identifying pollution sources and physical coefficients and the forward problem of inferring pollutant transport. Governed by advection, diffusion, and reaction processes, this transport phenomenon can be represented by the advection–diffusion–reaction (ADR) equation. In this paper, the physics-informed neural networks (PINNs) are applied to solve the forward and inverse ADR problems. To further enhance the stability and accuracy of the original PINN, two improvements are developed. The first adjusts the orthogonal grid (OG) point selection method and the other suggests adding an additional regulation function, namely, first derivative constraint (FDC). The new method is referred to as OG-PINN with FDC. To verify the effectiveness of the proposed method, five forward and inverse ADR problems are solved, and the results are compared with the analytical and reference solutions. For forward problems, the improved method can solve various ADR problems accurately and stably. For inverse problems, the ability of the OG-PINN for model parameter learning and initial distribution prediction is demonstrated and analyzed. The former gives the missed physical information in the ADR equation from the data, and the latter is used to trace the source of pollutants. The proposed method is quantitatively reliable for investigating various advection–diffusion–reaction processes.