  Numerical simulations of multiphase flows are crucial in numerous engineering
applications, but are often limited by the computationally demanding solution
of the Navier-Stokes (NS) equations. Here, we present a data-driven workflow
where a handful of detailed NS simulation data are leveraged into a
reduced-order model for a prototypical vertically falling liquid film. We
develop a physics-agnostic model for the film thickness, achieving a far better
agreement with the NS solutions than the asymptotic Kuramoto-Sivashinsky (KS)
equation. We also develop two variants of physics-infused models providing a
form of calibration of a low-fidelity model (i.e. the KS) against a few
high-fidelity NS data. Finally, predictive models for missing data are
developed, for either the amplitude, or the full-field velocity and even the
flow parameter from partial information. This is achieved with the so-called
"Gappy Diffusion Maps", which we compare favorably to its linear counterpart,
Gappy POD.
