Physics-informed neural networks for advection–diffusion–Langmuir adsorption processes

Advection–diffusion–Langmuir adsorption (ADLA) presents a complex problem in chemical engineering and biomedicine fields. This transport phenomenon can be described by the advection–diffusion–reaction (ADR) equations, which traditionally require intensive computational load at extreme conditions. In this paper, physics-informed neural networks (PINNs) are applied to solve the ADR equations due to their mesh-free and computationally efficient nature. Six cases are examined, including both diffusion-dominated and advection-dominated cases with varying Péclet numbers Pe and aspect ratios λ. To ensure stability and efficiency during training with the Adam optimizer, the gradients of the loss function are analyzed. Key gradient terms causing instability are identified, leading to recommendations for lower weights for these gradient terms. The validation results show that compared to the finite difference method, PINN achieves a concentration field error within 10% and an average adsorption amount error within 7.2% for diffusion-dominated cases. For advection-dominated cases, the errors are within 20% and 2.5%, respectively. In conclusion, PINNs can offer an efficient and accurate technique for solving ADR equations.