Solution of advection-diffusion-reaction inverse problems with Physics-Informed Neural Networks

Abstract

. In this work, two inverse problems related to pollutant dispersion in a river considering the advection-dispersion-reaction equation are studied along with a Neural Network approach. The first inverse problem concerns the estimation of the reaction parameter in an homogeneous equation, and the second one concerns the estimation of source pollution location in the non-homogeneous case. Both inverse problems are solved by two multiplayer perceptron networks: the usual Artificial Neural Network (ANN) and the Physics-Informed Neural Network (PINN), which is a special type of neural network that includes the physical laws that describes the phenomena in its formulation . Numerical experiments related to both inverse problems with ANN and with PINN are presented, demonstrating the feasibility of the proposed approach.