  The present study develops a physics-constrained neural network (PCNN) to
predict sequential patterns and motions of multiphase flows (MPFs), which
includes strong interactions among various fluid phases. To predict the order
parameters, which locate individual phases in the future time, a neural network
(NN) is applied to quickly infer the dynamics of the phases by encoding
observations. The multiphase consistent and conservative boundedness mapping
algorithm (MCBOM) is next implemented to correct the predicted order
parameters. This enforces the predicted order parameters to strictly satisfy
the mass conservation, the summation of the volume fractions of the phases to
be unity, the consistency of reduction, and the boundedness of the order
parameters. Then, the density of the fluid mixture is updated from the
corrected order parameters. Finally, the velocity in the future time is
predicted by another NN with the same network structure, but the conservation
of momentum is included in the loss function to shrink the parameter space. The
proposed PCNN for MPFs sequentially performs (NN)-(MCBOM)-(NN), which avoids
nonphysical behaviors of the order parameters, accelerates the convergence, and
requires fewer data to make predictions. Numerical experiments demonstrate that
the proposed PCNN is capable of predicting MPFs effectively.
