# Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations

arXiv: https://arxiv.org/abs/2604.08194 · HTML: https://mlsanity.com/paper/2604.08194/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 35 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [Deep Learning in Neural Networks: An Overview](https://mlsanity.com/paper/1404.7828/) (2014)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Scientific Machine Learning of Flow Resistance Using Universal Shallow Water Equations with Differentiable Programming](https://mlsanity.com/paper/2502.12396/) (2025)
- [Efficient numerical methods for the Maxey-Riley-Gatignol equations with Basset history term](https://mlsanity.com/paper/2403.13515/) (2024)
- [Relevance of the Basset history term for Lagrangian particle dynamics](https://mlsanity.com/paper/2407.01041/) (2024)

## Abstract (arXiv)

The Maxey-Riley-Gatignol equations (MaRGE) model the motion of spherical inertial particles in a fluid. They contain the Basset force, an integral term which models history effects due to the formation of wakes and boundary layer effects. This causes the force that acts on a particle to depend on its past trajectory and complicates the numerical solution of MaRGE. Therefore, the Basset force is often neglected, despite substantial evidence that it has both quantitative and qualitative impact on the movement patterns of modelled particles. Using the concept of universal differential equations, we propose an approximation of the history term via neural networks which approximates MaRGE by a system of ordinary differential equations that can be solved with standard numerical solvers like Runge-Kutta methods.