DropNet : A neural network solution to flow instabilities.

Forecasting phenomenon arising from nonlinear dynamical systems is a daunting task. Formal models are rarely analytically tractable and
numerical simulations are computationally expensive and exponentially sensitive to initial conditions. As a result, the details of the physics of those systems far from equilibrium remains elusive; prompting the need for the development of new tools. Neural networks have been at the foreground of the machine learning community for their versatility and ability to capture complex relationships and patterns in data. Further, predictions stemming from these trained networks are efficient since their computational complexity scales as a set of matrix-vector multiplications. However, the prediction accuracy of these models heavily relies on training with extensive dataset and scales accordingly to the number of samples in the latter. Here we propose an approach to rethink the traditional experimental setting in applied physics in favour of a data-driven framework. We focus on the study of fluid-mediated instabilities. We show that one can predict the spatial structure of droplets arising from a Rayleigh-Taylor instability and highlight several techniques to recover significant physical knowledge from the high dimensional models implemented.