Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
Estimation of pollution sources with Physics-Informed Neural Network
Submission Author:
Roberto Mamud Guedes da Silva , RJ
Co-Authors:
Roberto Mamud Guedes da Silva, Vinicius Albani, Helio Migon, Antônio Silva Neto
Presenter: Vinicius Albani
doi://10.26678/ABCM.ENCIT2022.CIT22-0108
Abstract
In this work, the inverse problem of identification of pollution sources location and intensity in a river is studied considering the advection-dispersion equation, along with a Neural Network approach. In the direct problem, the location and the intensity of the source terms are known as well as the PDE coefficients and then it is solved by classical numerical methods. The numerical solution is computed in random nodes in the domain with the aim of to generate a dataset representing a synthetic experimental data, where it will be used as input, noisy included, for the inverse problem and formulation. The inverse problem is posed as, given some measurements from sensors (synthetically generated) and the medium parameters, we want to estimate the pollutant source location. This problem is solved by two networks: the usual Artificial Neural Network (ANN) and the Physics-Informed Neural Network (PINN). In both cases we consider a network formed by Multi-Layer Perceptron in a fully-connected network. In the ANN approach, we construct a net that associates the concentration at the nodes as input to the source location as a output. First, we train the net, obtaining a optimal set of weights, and in a second step, we apply the net at the sensor measurement. This calculation is instantaneous and generate an estimation of source location. The numerical experiments using ANN are implemented, showing good results, even when considering noisy measurements. In the other hand, in the PINN approach, the measurements from the sensors are incorporated in the new loss function, where in this work, we also consider initial and boundary conditions in this optimization process. The PINN is a recent type of neural networks that are trained to solve some learning tasks while, at the same time, satisfies the physical laws that describes the phenomena involved. The present approach of constructing the loss function with points beyond those from measurements is slightly different from the original research paper that introduces the PINN framework. Numerical experiments related to estimation of source location are presented, with results not so good as those from ANN. Further experiments are necessary to improve the results of the present work.
Keywords
Inverse problem, machine learning, Physics-informed neural networks, Bayesian neural networks
