Approximation of the Basset force in the Maxey-Riley-Gatignol equations via universal differential equations
Citation Link: https://doi.org/10.15480/882.19150
Publikationstyp
Journal Article
Date Issued
2026-10-27
Sprache
English
TORE-DOI
Citation
Machine learning: science and technology (in Press): (2026)
Publisher DOI
Publisher
Institute of Physics (IOP)
Peer Reviewed
true
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. In particular, for long-term and high-resolution simulations of trajectories, where the number of required time-steps is large, the UDE approach can reduce time-to-solution.
Subjects
cs.LG
math.NA
DDC Class
510: Mathematics
Publication version
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