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

arXiv: https://arxiv.org/abs/2405.10442 · HTML: https://mlsanity.com/paper/2405.10442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 10 of 10)

- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems](https://mlsanity.com/paper/2203.15706/) (2022)
- [Deep learning to discover and predict dynamics on an inertial manifold](https://mlsanity.com/paper/2001.04263/) (2019)
- [Data-Driven Reduced-Order Modeling of Spatiotemporal Chaos with Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.00060/) (2021)
- [Data-driven control of spatiotemporal chaos with reduced-order neural ODE-based models and reinforcement learning](https://mlsanity.com/paper/2205.00579/) (2022)
- [Autoencoders for discovering manifold dimension and coordinates in data from complex dynamical systems](https://mlsanity.com/paper/2305.01090/) (2023)
- [Data-driven low-dimensional dynamic model of Kolmogorov flow](https://mlsanity.com/paper/2210.16708/) (2022)
- [Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network](https://mlsanity.com/paper/2206.13905/) (2022)

## Abstract (arXiv)

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 B, and was trained on a data set containing the evolution of fibers beginning at set angles of inclination. For the range of 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.