Convolutional feature-enhanced physics-informed neural networks for the spatio-temporal reconstruction of two-phase flows

Two-phase flow phenomena play a key role in numerous technical processes, including hydrogen fuel cells, spray cooling techniques and combustion. Optical measurement techniques, such as shadowgraphy and particle image velocimetry, provide insight through the measurement of the gas-liquid interface and internal velocity fields, respectively. However, these experiments are constrained to planar measurements, whereas the dynamics of the flow are generally three-dimensional (3D). Deep learning techniques based on convolutional neural networks offer a pathway for volumetric reconstruction of the experiments by leveraging spatial structure in the images and context-rich feature extraction. Physics-informed neural networks (PINNs) emerge as a promising alternative, as they incorporate prior knowledge encoded in the networks by training on governing equations, allowing for accurate predictions even from limited data. We propose a novel approach for convolutional feature-enhanced PINNs for the spatio-temporal reconstruction of two-phase flows from shadowgraphy images. The capability of the novel method is demonstrated by the accurate reconstruction of the 3D gas-liquid interface, velocity and pressure fields for an impinging droplet based on planar experimental data.