Learning by neural networks under physical constraints for simulation in fluid mechanics

The Physical Informed Neural Networks (PINN) model is one of the emerging and promising Deep Learning approaches to predict physical phenomena governed by PDEs such as fluid flow dynamics. The PINN model is indeed of great importance for improving the accuracy of machine learning methods for predicting mass transfer problems. However, it is sensitive to the accuracy of input datasets, and also struggles to predict phenomena occurring in complex geometries. These two weaknesses could limit the application of the PINN model. In this article, we improve the use of the PINN model by combining it with a One-hot matrix model to better take into account the boundary conditions on complex geometries. The use of the One-hot matrix is also investigated with non-uniform weights from physics. We indeed used the Q-criterion as a non-uniform weight to enforce the vortical structure location by the neural network. The proposed model more accurately predicts the two-dimensional flow around sharp rectangular obstacles from low-resolution datasets.

Automated summary

The Physical Informed Neural Networks (PINN) model is a promising deep learning approach for predicting physical phenomena governed by PDEs, especially for improving the accuracy of mass transfer problem predictions. However, it is sensitive to input dataset accuracy and struggles with predicting phenomena in complex geometries. In this article, the use of the PINN model is improved by combining it with a One-hot matrix model to better account for boundary conditions in complex geometries. The use of non-uniform weights from physics, such as the Q-criterion, is also investigated. The proposed model accurately predicts two-dimensional flows around sharp rectangular obstacles from low-resolution datasets.