  In this work, physics-informed neural networks are applied to incompressible
two-phase flow problems. We investigate the forward problem, where the
governing equations are solved from initial and boundary conditions, as well as
the inverse problem, where continuous velocity and pressure fields are inferred
from scattered-time data on the interface position. We employ a volume of fluid
approach, i.e. the auxiliary variable here is the volume fraction of the fluids
within each phase. For the forward problem, we solve the two-phase Couette and
Poiseuille flow. For the inverse problem, three classical test cases for
two-phase modeling are investigated: (i) drop in a shear flow, (ii) oscillating
drop and (iii) rising bubble. Data of the interface position over time is
generated by numerical simulation. An effective way to distribute spatial
training points to fit the interface, i.e. the volume fraction field, and the
residual points is proposed. Furthermore, we show that appropriate weighting of
losses associated with the residual of the partial differential equations is
crucial for successful training. The benefit of using adaptive activation
functions is evaluated for both the forward and inverse problem.
