  Micro-bubbles and bubbly flows are widely observed and applied in chemical
engineering, medicine, involves deformation, rupture, and collision of bubbles,
phase mixture, etc. We study bubble dynamics by setting up two numerical
simulation cases: bubbly flow with a single bubble and multiple bubbles, both
confined in the microchannel, with parameters corresponding to their medical
backgrounds. Both the cases have their medical background applications.
Multiphase flow simulation requires high computation accuracy due to possible
component losses that may be caused by sparse meshing during the computation.
Hence, data-driven methods can be adopted as an useful tool. Based on
physics-informed neural networks (PINNs), we propose a novel deep learning
framework BubbleNet, which entails three main parts: deep neural networks (DNN)
with sub nets for predicting different physics fields; the
semi-physics-informed part, with only the fluid continuum condition and the
pressure Poisson equation $\mathcal{P}$ encoded within; the time discretized
normalizer (TDN), an algorithm to normalize field data per time step before
training. We apply the traditional DNN and our BubbleNet to train the coarsened
simulation data and predict the physics fields of both the two bubbly flow
cases. The BubbleNets are trained for both with and without $\mathcal{P}$, from
which we conclude that the 'physics-informed' part can serve as inner
supervision. Results indicate our framework can predict the physics fields more
accurately, estimating the prediction absolute errors. Our deep learning
predictions outperform traditional numerical methods computed with similar data
density meshing. The proposed network can potentially be applied to many other
engineering fields.
