Deep Learning Methods for Q Field Reconstruction Using Vortex Axes

The importance of turbulence and vortex dynamics research is well observed in the fact that there is still no perfect way to correlate a true vortex and its axis with a complete flow field. Aiming to find a one-to-one mapping between these two could hold a key to devising efficient algorithms to store memory-intensive turbulent flow data (Q field) in a smaller format that only contains vortex axis (obtained using VATIP) and allows for efficient reconstruction of the initial field. Of immense potential are machine learning (ML) algorithms that can learn and correlate patterns between these two sets of data. One such ML algorithm was devised using two modified versions of variational autoencoders (VAEs) that were altered to be suited for the regression task of Q field reconstruction from the extremely sparse VATIP data. This model gave R2 scores of 0.1947 and 0.0342 on a small and large VATIP-Q field dataset with predictions that were visually similar to the true targets. Though, a significant challenge still remains of finding a model that, unlike the one currently devised, does not overfit and is robust to the data.