  Accurate prediction of the dynamics and deformation of freely moving drops is
crucial for numerous droplet applications. When the Weber number is finite but
below a critical value, the drop deviates from its spherical shape and deforms
as it is accelerated by the gas stream. Since aerodynamic drag on the drop
depends on its shape oscillation, accurately modeling the drop shape evolution
is essential for predicting the drop's velocity and position. In this study, 2D
axisymmetric interface-resolved simulations were performed to provide a
comprehensive dataset for developing a data-driven model. Parametric
simulations were conducted by systematically varying the drop diameter and
free-stream velocity, achieving wide ranges of Weber and Reynolds numbers. The
instantaneous drop shapes obtained in simulations are characterized by
spherical harmonics. Temporal data of the drag and modal coefficients are
collected from the simulation data to train a Nonlinear Auto-Regressive models
with eXogenous inputs (NARX) neural network model. The overall model consists
of two multi-layer perceptron networks, which predict the modal coefficients
and the drop drag, respectively. The drop shape can be reconstructed with the
predicted modal coefficients. The model predictions are validated against the
simulation data in the testing set, showing excellent agreement for the
evolutions of both the drop shape and drag.
