Data-driven low-dimensional model of a sedimenting flexible fiber

Abstract

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. In this paper, we describe 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 dataset. The approach combines an autoencoder neural network architecture to learn a low-dimensional latent representation of the filament shape, with a neural ordinary differential equation that learns the evolution of the particle in the latent state. The model was designed to model filaments of varying flexibility, characterized by an elastogravitational number $\mathcal{B}$, and was trained on a dataset containing the evolution of fibers beginning at set angles of inclination. For the range of $\mathcal{B}$ considered here (100–10 000), the filament shape dynamics can be represented with high accuracy with only four degrees of freedom, in contrast with 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 elastogravitational numbers.