Machine learning for hydrodynamic stability

Abstract: A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The objective is to exploit shallow neural networks for a binary classification task to distinguish between bifurcated and non-bifurcated states. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to a bifurcating indicator identifying the region of interest. The computational procedure is demonstrably robust and does not require parameter tuning. The essential feature of the strategy is that the computational solution of the Navier-Stokes equations is a reliable proxy for laboratory experiments investigating sensitivity to flow parameters. The applicability of our bifurcation detection strategy is demonstrated by an investigation of two classical examples of flow instability associated with thermal convection. The codes used to generate and process the labelled data are available on GitHub.