  The onset of hydrodynamic instabilities is of great importance in both
industry and daily life, due to the dramatic mechanical and thermodynamic
changes for different types of flow motions. In this paper, modern machine
learning techniques, especially the convolutional neural networks (CNN), are
applied to identify the transition between different flow motions raised by
hydrodynamic instability, as well as critical non-dimensionalized parameters
for characterizing this transit. CNN not only correctly predicts the critical
transition values for both Taylor-Couette (TC) flow and Rayleigh- B\'enard (RB)
convection under various setups and conditions, but also shows an outstanding
performance on robustness and noise-tolerance. In addition, key spatial
features used for classifying different flow patterns are revealed by the
principal component analysis.
