  The present work introduces a deep learning approach for the
three-dimensional reconstruction of the spatio-temporal dynamics of the
gas-liquid interface in two-phase flows on the basis of monocular images
obtained via optical measurement techniques. The dynamics of liquid droplets
impacting onto structured solid substrates are captured through high-speed
imaging in an extended shadowgraphy setup with additional reflective glare
points from lateral light sources that encode further three-dimensional
information of the gas-liquid interface in the images. A neural network is
learned for the physically correct reconstruction of the droplet dynamics on a
labelled dataset generated by synthetic image rendering on the basis of
gas-liquid interface shapes obtained from direct numerical simulation. The
employment of synthetic image rendering allows for the efficient generation of
training data and circumvents the introduction of errors resulting from the
inherent discrepancy of the droplet shapes between experiment and simulation.
The accurate reconstruction of the gas-liquid interface during droplet
impingement on the basis of images obtained in the experiment demonstrates the
practicality of the presented approach based on neural networks and synthetic
training data generation. The introduction of glare points from lateral light
sources in the experiments is shown to improve the reconstruction accuracy,
which indicates that the neural network learns to leverage the additional
three-dimensional information encoded in the images for a more accurate depth
estimation. Furthermore, the physically reasonable reconstruction of unknown
gas-liquid interface shapes indicates that the neural network learned a
versatile model of the involved two-phase flow phenomena during droplet
impingement.
