Neural Networks as Globally Optimal Multilayer Convolution Architectures for Learning Fluid Flows

In this work we explore the advantages of end-to-end learning of multilayer maps offered by feed forward neural-networks (FFNN) for learning and predicting dynamics from transient fluid flow data.While machine learning in general depends on data quality and quantity relative to the underlying dynamics of the system, it is important for a given learning architecture to make the most of this available information. To this end, we focus on data-driven problems where there is a need to predict over reasonable time into the future with limited data availability. Such function approximation or time series prediction is in contrast to many applications of machine learning such as pattern recognition and parameter estimation that leverage vast datasets. In this study, we interpret the suite of recently popular data-driven learning approaches that approximate the dynamics as Markov linear model in a higher-dimensional feature space as a multilayer architecture similar to neural networks.