Estimation of scalar source and associated scalar field based on limited measurement data by using physics-informed neural networks

摘要

Physic-Informed Neural Networks (PINN) are used to estimate the location and intensity of scalar-sources as well as the resultant concentration distribution based on limited measurement data. First, numerical simulations are performed to reproduce the velocity and scalar fields with a scalar source in a 2D plane. The obtained velocity and scalar fields are used as the ground truth, whereas the values of the scalar concentration at sparse and limited locations are extracted as measurement data. Then, PINN is trained by using the measurement data with a constrain of the scalar transport equation. It is shown that PINN provides a useful framework for predicting the scalar source and the resultant concentration field by integrating measurement data and underlying physical laws.