Machine learning for hydrodynamic stability

TL;DR

This paper introduces a machine learning approach to assess fluid flow stability by mapping flow parameters to bifurcation probabilities, offering a robust, parameter-tuning-free method validated on classical thermal convection examples.

Contribution

The paper presents a novel machine learning framework that reliably predicts flow bifurcations from Navier-Stokes solutions without parameter tuning, applicable to classical flow instability problems.

Findings

Robust probabilistic bifurcation detection method.

Validated on thermal convection flow examples.

Codes available on GitHub for reproducibility.

Abstract

A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing the probability of observing a bifurcated solution. 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 probabilistic 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.