  The dynamics of flexible filaments entrained in flow, important for
understanding many biological and industrial processes, are computationally
expensive to model with full-physics simulations. This work describes a
data-driven technique to create high-fidelity low-dimensional models of
flexible fiber dynamics using machine learning; the technique is applied to
sedimentation in a quiescent, viscous Newtonian fluid, using results from
detailed simulations as the data set. The approach combines an autoencoder
neural network architecture to learn a low-dimensional latent representation of
the filament shape, with a neural ODE that learns the evolution of the particle
in the latent state. The model was designed to model filaments of varying
flexibility, characterized by an elasto-gravitational number $\mathcal{B}$, and
was trained on a data set containing the evolution of fibers beginning at set
angles of inclination. For the range of $\mathcal{B}$ considered here
(100-10000), the filament shape dynamics can be represented with high accuracy
with only four degrees of freedom, in contrast to the 93 present in the
original bead-spring model used to generate the dynamic trajectories. We
predict the evolution of fibers set at arbitrary angles and demonstrate that
our data-driven model can accurately forecast the evolution of a fiber at both
trained and untrained elasto-gravitational numbers.
