Computational methods in fluid research have been progressing during the past few years, driven by the incorporation of massive amounts of data, either in textual or graphical form, generated from multi-scale simulations, laboratory experiments, and real data from the field. Artificial Intelligence (AI) and its adjacent field, Machine Learning (ML), are about to reach standardization in most fields of computational science and engineering, as they provide multiple ways for extracting information from data that turn into knowledge, with the aid of portable software implementations that are easy to adopt. There is ample information on the historical and mathematical background of all aspects of AI/ML in the literature. Thus, this review article focuses mainly on their impact on fluid research at present, highlighting advances and opportunities, recognizing techniques and methods having been proposed, tabulating, and testing some of the most popular algorithms that have shown significant accuracy and performance on fluid applications. We also investigate algorithmic accuracy on several fluid datasets that correspond to simulation results for the transport properties of fluids and suggest that non-linear, decision tree-based methods have shown remarkable performance on reproducing fluid properties.

We consider the family of infinite positive Borel measures $\mu $ in the unit disc, with finite degree of contact at the unit circle, and the set $E_{\mu }$ of points in the unit circle for which every neighborhood contains infinite mass of $\mu $ . Assuming that $E_{\mu }$ is a Carleson set, we show that all Blaschke sequences are zero sets for the corresponding Dirichlet space $D_{\mu }$ .