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

Abstract

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)

From partial data to out-of-sample parameter and observation estimation with diffusion maps and geometric harmonics

“…In the case where the data live in a curved manifold, the size of the POD basis required for accurate reconstruction of the data is expected to be high, since several hyperplanes are necessary to describe it; this will be discussed briefly in a subsequent section. This drawback is addressed with DMAPs, which typically require less coordinates than its linear counterpart, to accurately capture the data variance (Martin-Linares et al, 2023).…”