Classifying Turbulent Environments via Machine Learning

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g. it is important for the selection of optimal control policies trained in different turbulent backgrounds, to predict the probability of extreme events and/or to infer physical parameters labeling the different turbulent set-ups. To achieve such a goal one can use different tools depending on the system's knowledge and on the quality and quantity of the accessible data. In this context, we assume to work in a model-free setup completely blind to all dynamical laws, but with a large quantity of (good quality) data for training. As a prototype of complex flows with different attractors and different multi-scale statistical properties, we selected 10 turbulent 'ensembles' by changing the rotation frequency of the frame of reference of a 3d domain. We are supposed to have access to a set of partial observations limited to the instantaneous kinetic energy distribution in a 2d plane, as is often the case in geophysics and astrophysics. We compare results obtained by a Machine Learning (ML) approach consisting of a state-of-the-art Deep Convolutional Neural Network (DCNN) against Bayesian inference which exploits the information on velocity and enstrophy moments. First, we discuss the supremacy of the ML approach, presenting also results changing the number of training data and of the hyper-parameters. Second, we present an ablation study on the input data aimed to perform a ranking on the importance of the flow features used by the DCNN, helping to identify the main physical contents used by the classifier. Finally, we discuss the main limitations of such data-driven methods and potential interesting applications.