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 process, this transport phenomenon can be represented by the advection-diffusion-reaction (ADR) equation. In this paper, the physics-informed neural networks (PINN) is 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 are 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.

PINN-CDR: A Neural Network-Based Simulation Tool for Convection-Diffusion-Reaction Systems

“…Due to the similar computational complexity of the two models, the network structure is set to be the same in all the tests. Referring to the cases in the references [23,43], the network structure in this study is as follows: seven hidden layers and 100 neurons in each layer. More hidden layers and more neurons have been tested, but no signifcant diferences were observed.…”

“…PINN has been successfully used for solving PDEs or complex PDE-based problems in various domains, such as fuid mechanics [38,39], medical diagnosis [40,41] and materialogy [42]. PINN has been applied to single reactant CDR problems with good results [43]. However, there are no researches on the application of PINN to CDR systems with multiple coupled reactants.…”

The Application of Physics-Informed Machine Learning in Multiphysics Modeling in Chemical Engineering

“…The results showed that it was able to identify an unknown effectiveness factor with an error of 0.3%, even for a small number of observation datasets. Hou et al 160 introduced two improvements to the original PINN method: adjusting the orthogonal grid (OG) point selection method and incorporating an additional regularization function called the first derivative constraint (FDC). This modified approach, known as OG-PINN with FDC, was specifically applied to address both forward and inverse advection−diffusion reaction (ADR) problems.…”

Physics‐informed learning of chemical reactor systems using decoupling–coupling training framework

“…Previous studies have primarily focused on modeling intrinsic kinetics through solving low-dimensional ODEs for various reactions, such as ethylbenzene to styrene, 25 coal gasification, 26 CO 2 methanation, 27,28 and advection-diffusion. 29 However, these intrinsic kinetics models only considered the relationship between reaction rates and reactant concentrations, disregarding the influence of heat and mass transfer on reaction kinetics. In recent studies, the potential use of PINN method was explored to incorporate the conservation of mass, momentum, energy, and species transport in modeling chemical reactors, such as the tubular reactor with a series reaction 30 and the continuously stirred tank reactor with a van de Vusse reaction.…”

“…To begin with, it is crucial to address a research gap that can accurately characterize and capture the multiphysics coupling effect present in chemical reactors, 24 specifically focusing on the intricate interplay between reaction kinetics and heat and mass transfer. Previous studies have primarily focused on modeling intrinsic kinetics through solving low‐dimensional ODEs for various reactions, such as ethylbenzene to styrene, 25 coal gasification, 26 CO 2 methanation, 27,28 and advection‐diffusion 29 . However, these intrinsic kinetics models only considered the relationship between reaction rates and reactant concentrations, disregarding the influence of heat and mass transfer on reaction kinetics.…”