Parameter estimation in the pollutant dispersion problem with Physics-Informed Neural Networks

Abstract

In this work, the inverse problem of parameter estimation in the advection-dispersion-reaction equation, modelling the pollutant dispersion in a river, is studied with a Neural Network approach. In the direct problem, the dispersion, velocity and reaction parameters are known and then the initial and boundary value problem is solved by classical numerical methods, where it is used as input dataset for the inverse problem and formulation. In the inverse problem, we know the dispersion and the velocity parameters and also the information about the pollutant concentration from the synthetic experimental data, and then the aim is to estimate the reaction parameter in the advection-dispersion-reaction equation. This inverse problem is solved by an usual Artificial Neural Network (ANN) and by a Physics-Informed Neural Network (PINN), which is a special type of neural networks that includes in its formulation the physical laws that describe the phenomena involved. Numerical experiments with both the ANN and PINN are presented, demonstrating the feasibility of the approach considered.