On Limitations of Several Approaches for Correcting Coarse Flow Simulations With Machine Learning Techniques

This paper explores several methods intended to predict corrections to improve coarse grid solutions of a flow field. Motivated by applications in hemodynamics, this flow is on the transition to turbulence, and simulations are performed on unstructured tetrahedral grids. The predictions are based on learning deep neural networks with differences of coarse and fine grid solutions. Two kinds of feedforward networks, several graph neural networks, and a hierarchical neural network are studied. To simplify the task, the correction of the statistically steady state is considered. However, even then, all studied approaches fail to produce useful results in the validation step, which reveals limitations of current deep learning approaches to predict coarse grid corrections for complicated flow problems.