Learning the correction factor in closed macroscale equations using conventional neural networks

We use conventional neural networks (CNNs) to estimate the correction factor in closed macroscale equations. Presence of nonlinear operator poses a great challenge in direct computation of the closure factor using conventional analytical techniques. To tackle this problem, we develop a deep architecture that can identify the key points in streamlines and map them to the correction factor. We feed the snapshots of the microscale field to the deep neural network in order to predict the correction factor. To improve the fidelity of the prediction, we identify some source terms arising from the upscale PDEs and boundary conditions and add them to the output of the CNN and input of the feed forward network deep network. We show that this architecture can map the snapshot of the field to the correction factor with high fidelity. In fact, the effect of the source terms contribution on fidelity is more prominent than the field grid resolution. The advantageous of this framework is that one can estimate the high-fidelity correction factor without knowing the physical parameters of system.