  Neural networks in fluid mechanics offer an efficient approach for exploring
complex flows, including multiphase and free surface flows. The recurrent
neural network, particularly the Long Short-Term Memory (LSTM) model, proves
attractive for learning mappings from transient inputs to dynamic outputs. This
study applies LSTM to predict transient and static outputs for fluid flows
under surface tension effects. Specifically, we explore two distinct droplet
dynamic scenarios: droplets with diverse initial shapes impacting with solid
surfaces, as well as the coalescence of two droplets following collision. Using
only dimensionless numbers and geometric time series data from numerical
simulations, LSTM predicts the energy budget. The marker-and-cell
front-tracking methodology combined with a marker-and-cell finite-difference
strategy is adopted for simulating the droplet dynamics. Using a recurrent
neural network (RNN) architecture fed with time series data derived from
geometrical parameters, as for example droplet diameter variation, our study
shows the accuracy of our approach in predicting energy budgets, as for
instance the kinetic, dissipation, and surface energy trends, across a range of
Reynolds and Weber numbers in droplet dynamic problems. Finally, a two-phase
sequential neural network using only geometric data, which is readily available
in experimental settings, is employed to predict the energies and then use them
to estimate static parameters, such as the Reynolds and Weber numbers. While
our methodology has been primarily validated with simulation data, its
adaptability to experimental datasets is a promising avenue for future
exploration. We hope that our strategy can be useful for diverse applications,
spanning from inkjet printing to combustion engines, where the prediction of
energy budgets or dissipation energies is crucial.
