Physics-agnostic and physics-infused machine learning for thin films flows: modelling, and predictions from small data

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. The development of surrogate models relies on involved algebra and several assumptions. 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 favourably to its linear counterpart, gappy POD.